If p: All integers are rational numbers and q: Every rational number is an integer, then which of the following

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p is false and q is true

p is true and q is false

Both the p and q are true

Both p and q are false

answer is B.

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Detailed Solution

Concept- The variety of the form of pq integer is the wide variety that has an integer value and usually comes within the total variety of numbers from −∞ to ∞.
All integers are rational number however all rational numbers are not integers, as we understand rational quantity can be written as p/q
And integers, entire positive and bad numbers on the quantity line.
Now, to take an example of any rational variety which is not an integer is:3/4
Here, the instance taken into consideration by means of us as 3/4 is not an integer but nonetheless a rational wide variety.
Now, to show that it isn't always an integer, locate the decimal cost of the range considered as:3/4=0.seven five
So, it gives the price zero.7/5 and with the aid of the definition of integers, it isn't always an integer price.
But whilst we pass for the definition of rational number, 3/4 is of the form p/q and also its denominator isn't always zero which states that it's miles a legitimate rational variety proves q assertion is false.
sooner or later, if we take any integer fee let us suppose 2, so we can write it inside the shape as:2/1
So, it gives the rational shape as p/q and its denominator isn't always 0 proves the assertion p is actual.
Hence, the correct option is 2.

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