First slide

Introduction to mathematical reasoning

Question

Let A,B,C and D be four non-empty sets. The contrapositive statement of “If $A \subseteq B$ and $B \subseteq D$ , then $A \subseteq C$ ” is :

Easy

A

If $A \subseteq C$ ,then $B \subset A$ and $D \subset B$
B

If $A \subseteq C$ ,then $A \subseteq B$ and $B \subseteq D$
C

If $A \subseteq C$ ,then $B \subseteq D$ and $A \subseteq B$
D

If $A \subseteq C$ ,then $A \subseteq B$ or $B \subseteq D$

Solution

Contrapositive of $p \to q$ is $~ q \to ~ p$
$(A \subseteq B) \land (B \subseteq D) \to (A \subseteq C)$
Contrapositive is
$~ (A \subseteq C) \to ~ (A \subseteq B) \lor ~ (B \subseteq D)$
$(A \subseteq C) \to (A \subseteq B) \lor (B \subseteq D)$

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