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Q.
Which of the following statements is false?
Mathematical Reasoning
Solution:
(a) The component statements are
$p :\sqrt{2}$ is a rational number.
$q : \sqrt{2}$ is an irrational number.
Here, we know that the first statement is false and the second is true and "Or" is exclusive, so the compound statement is true.
(b) The component statements are
$p :$ To get into a public library, children need an identity card.
$q :$ To get into a public library, children need a letter from the school authorities.
Children can enter the library if they have either of the two, an identity card or the letter, as well as when they have both. Therefore, it is inclusive "Or". The compound
statement is also true.
(c) Here "Or" is exclusive. When we look at the component statements, we get that the statement is true.
(d) $p :$ Pune is the capital of Kolkata.
$q :$ Pune is the capital of Karnataka.
Both these statements are false. So compound statement is also false.