Write the truth values of the following statements:i. The square of an

1.	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» 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.

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»

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.