{"id":155580,"date":"2022-03-26T00:48:16","date_gmt":"2022-03-25T19:18:16","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/statements-in-mathematical-reasoning\/"},"modified":"2022-12-31T14:52:04","modified_gmt":"2022-12-31T09:22:04","slug":"statements-in-mathematical-reasoning","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/maths\/statements-in-mathematical-reasoning\/","title":{"rendered":"Statements in Mathematical Reasoning"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_37 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" style=\"display: none;\"><label for=\"item\" aria-label=\"Table of Content\"><span style=\"display: flex;align-items: center;width: 35px;height: 30px;justify-content: center;\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/label><input type=\"checkbox\" id=\"item\"><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1' style='display:block'><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/statements-in-mathematical-reasoning\/#Mathematical_Reasoning\" title=\"Mathematical Reasoning\">Mathematical Reasoning<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/statements-in-mathematical-reasoning\/#What_is_a_Mathematical_Reasoning_Statement\" title=\"What is a Mathematical Reasoning Statement?\">What is a Mathematical Reasoning Statement?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/statements-in-mathematical-reasoning\/#Types_of_Maths_Reasoning_Statements\" title=\"Types of Maths Reasoning Statements\">Types of Maths Reasoning Statements<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/statements-in-mathematical-reasoning\/#Simple_Statements\" title=\"Simple Statements\">Simple Statements<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/statements-in-mathematical-reasoning\/#Compound_Statements\" title=\"Compound Statements\">Compound Statements<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/statements-in-mathematical-reasoning\/#Connectives_used_in_Compound_Statements\" title=\"Connectives used in Compound Statements:\">Connectives used in Compound Statements:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/statements-in-mathematical-reasoning\/#Mathematical_Reasoning_Formulas_used_in_Compound_Statements\" title=\"Mathematical Reasoning Formulas used in Compound Statements:\">Mathematical Reasoning Formulas used in Compound Statements:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/statements-in-mathematical-reasoning\/#Conditional_Statements\" title=\"Conditional Statements:\">Conditional Statements:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/statements-in-mathematical-reasoning\/#Inverse_Converse_and_Contrapositive_of_Conditional_statements\" title=\"Inverse, Converse, and Contrapositive of Conditional statements:\">Inverse, Converse, and Contrapositive of Conditional statements:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/statements-in-mathematical-reasoning\/#Mathematical_Reasoning_Formulas_of_Conditional_Statements\" title=\"Mathematical Reasoning Formulas of Conditional Statements:\">Mathematical Reasoning Formulas of Conditional Statements:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/statements-in-mathematical-reasoning\/#Mathematical_Reasoning_Questions\" title=\"Mathematical Reasoning Questions:\">Mathematical Reasoning Questions:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-12\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/statements-in-mathematical-reasoning\/#Validity_of_the_Statement\" title=\"Validity of the Statement\">Validity of the Statement<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-13\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/statements-in-mathematical-reasoning\/#Do_You_Know_What_an_Open_Statement_Is\" title=\"Do You Know What an Open Statement Is?\">Do You Know What an Open Statement Is?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-14\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/statements-in-mathematical-reasoning\/#Points_to_Remember\" title=\"Points to Remember\">Points to Remember<\/a><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"Mathematical_Reasoning\"><\/span>Mathematical Reasoning<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Mathematical reasoning is the process of using mathematical concepts and principles to solve problems. This can involve solving equations, modeling data, or analyzing patterns. Mathematical reasoning is a critical skill for students to learn, as it can be applied to a variety of real-world situations.<\/p>\n<p><img loading=\"lazy\" class=\"aligncenter wp-image-155579 size-full\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/statements-in-mathematical-reasoning.jpg\" alt=\"\" width=\"606\" height=\"428\" srcset=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/statements-in-mathematical-reasoning.jpg?v=1648235891 606w, https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/statements-in-mathematical-reasoning-300x212.jpg?v=1648235891 300w\" sizes=\"(max-width: 606px) 100vw, 606px\" \/><\/p>\n<h2><span class=\"ez-toc-section\" id=\"What_is_a_Mathematical_Reasoning_Statement\"><\/span>What is a Mathematical Reasoning Statement?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>A mathematical reasoning statement is a statement that uses mathematics to make a point. Mathematical reasoning statements can be used to solve problems, prove mathematical theorems, or just to illustrate a point. Mathematical reasoning statements are often written in the form of an equation or a proof.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Types_of_Maths_Reasoning_Statements\"><\/span>Types of Maths Reasoning Statements<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>A maths reasoning statement is a statement that uses mathematical symbols and concepts to express a logical argument. There are many different types of maths reasoning statements, including:<\/p>\n<p>\u00b7 Conditional Statements: A conditional statement is a statement that connects two statements using the word &#8220;if.&#8221; The first statement is the hypothesis, and the second statement is the conclusion. If the hypothesis is true, then the conclusion must be true as well.<\/p>\n<p>\u00b7 Inverse Statements: An inverse statement is a statement that connects two statements using the word &#8220;not.&#8221; The first statement is the hypothesis, and the second statement is the conclusion. If the hypothesis is true, then the conclusion must be false.<\/p>\n<p>\u00b7 Contrapositive Statements: A contrapositive statement is a statement that connects two statements using the word &#8220;not.&#8221; The first statement is the hypothesis, and the second statement is the conclusion. If the hypothesis is false, then the conclusion must be true.<\/p>\n<p>\u00b7 Logical Equivalents: Two statements are logically equivalent if they have the same truth value. If both statements are true, then they are logically equivalent. If both statements are false, then they are logically equivalent.<\/p>\n<p>\u00b7 Implication Statements: An implication statement is a statement that connects two statements using the word &#8220;implies.&#8221; The first statement is the hypothesis, and the second statement is the conclusion. If the hypothesis is true, then the conclusion must be true as well.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Simple_Statements\"><\/span>Simple Statements<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>A statement is a sentence that states a fact or asks a question.<\/p>\n<p>Statement Examples<\/p>\n<p>The sky is blue.<\/p>\n<p>Do you want to go to the store?<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Compound_Statements\"><\/span>Compound Statements<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>A compound statement is a group of two or more simple statements that are connected by operators such as and, or, and not.<\/p>\n<p>Statement 1; statement 2; statement 3<\/p>\n<p>Statement 1 and statement 2 are connected by the and operator, and statement 3 is connected by the or operator.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Connectives_used_in_Compound_Statements\"><\/span>Connectives used in Compound Statements:<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>and, or, but, not<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Mathematical_Reasoning_Formulas_used_in_Compound_Statements\"><\/span>Mathematical Reasoning Formulas used in Compound Statements:<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>1. If p then q<br \/>\n2. If and only if p then q<br \/>\n3. If p then q else r<br \/>\n4. If p then q else r if s<br \/>\n5. If p then q else r if not s<br \/>\n6. If p then q else r<br \/>\n7. If and only if p then q<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Conditional_Statements\"><\/span>Conditional Statements:<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>If you want to eat healthy, you should eat fruits and vegetables.<\/p>\n<p>If it is sunny outside, I will go for a walk.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Inverse_Converse_and_Contrapositive_of_Conditional_statements\"><\/span>Inverse, Converse, and Contrapositive of Conditional statements:<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Inverse: if P then Q<\/p>\n<p>Inverse: if not Q then not P<\/p>\n<p>Converse: if Q then P<\/p>\n<p>Converse: if not P then not Q<\/p>\n<p>Contrapositive: if not P then not Q<\/p>\n<p>Contrapositive: if Q then not P<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Mathematical_Reasoning_Formulas_of_Conditional_Statements\"><\/span>Mathematical Reasoning Formulas of Conditional Statements:<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The formulas for conditional statements are &#8220;if then&#8221; and &#8220;if and only if.&#8221; The symbol for &#8220;if then&#8221; is &#8220;\u2192,&#8221; and the symbol for &#8220;if and only if&#8221; is &#8220;\u2194.&#8221;<\/p>\n<p>&#8220;If then&#8221; is read as &#8220;if then .&#8221; It is a statement that says if one condition is met, then another condition is also met.<\/p>\n<p>&#8220;If and only if&#8221; is read as &#8220;if and only if.&#8221; It is a statement that says that the two conditions are both met.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Mathematical_Reasoning_Questions\"><\/span>Mathematical Reasoning Questions:<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>1. If x is an integer, what is the value of x?<\/p>\n<p>2. What is the value of x if x is a negative number?<\/p>\n<p>3. What is the value of x if x is a decimal?<\/p>\n<p>4. What is the value of x if x is a fraction?<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Validity_of_the_Statement\"><\/span>Validity of the Statement<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>There is no evidence to support the statement.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Do_You_Know_What_an_Open_Statement_Is\"><\/span>Do You Know What an Open Statement Is?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>An open statement is a statement that is not closed.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Points_to_Remember\"><\/span>Points to Remember<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Some key points to remember about the ketogenic diet:<\/p>\n<p>The ketogenic diet is a high-fat, moderate-protein, and low-carbohydrate diet.<\/p>\n<p>The ketogenic diet is used to treat seizures in children and adults.<\/p>\n<p>The ketogenic diet is also used to treat obesity, heart disease, and diabetes.<\/p>\n<p>The ketogenic diet is a high-fat, low-carbohydrate diet.<\/p>\n<p>The ketogenic diet is a weight-loss diet.<\/p>\n<p>The ketogenic diet is a low-carbohydrate diet.<\/p>\n<p>The ketogenic diet is a healthy diet.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Mathematical Reasoning Mathematical reasoning is the process of using mathematical concepts and principles to solve problems. This can involve solving [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_focuskw":"Statements in Mathematical Reasoning","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"Learn Statements in Mathematical Reasoning topic of Maths in details explained by subject experts on infinitylearn.com.","custom_permalink":"maths\/statements-in-mathematical-reasoning\/"},"categories":[13],"tags":[],"table_tags":[],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v17.9 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Statements in Mathematical Reasoning - Infinity Learn by Sri Chaitanya<\/title>\n<meta name=\"description\" content=\"Learn Statements in Mathematical Reasoning topic of Maths in details explained by subject experts on infinitylearn.com.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/statements-in-mathematical-reasoning\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Statements in Mathematical Reasoning - 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