Question

Write the truth values of the following statements:

i. The square of any odd number is even or the cube of any even number is even.

ii. \(\sqrt{5}\) is irrational but 3 + \(\sqrt{5}\) is a complex number.

iii. \(\exists\) n \(\in\) N, such that n + 5 > 10.

Answer 1

i. Let p: The square of any odd number is even.

q: The cube of any even number is even.

\(\therefore\)The symbolic form of the given statement is p \(\lor\) q.

Since the truth value of p is F and that of q is T,

\(\therefore\) truth value of p \(\lor\) q is T

ii. Let p: \(\sqrt{5}\) is irrational.

q: 3 +\(\sqrt{5}\) is a complex number.

\(\therefore\) The symbolic form of the given statement is

p \(\land\) q

Since the truth value of p is T and that of q is F,

\(\therefore\) truth value of p \(\land\) q is F.

iii. Consider the statement, \(\exists\) n \(\in\) N, n + 5 > 10

Clearly n \(\geq\)6, n\(\in\)N satisfy n + 5 > 10.

\(\therefore\) its truth value is T.