Question

Find the truth value of the following statements.

i. 14 is a composite number or 15 is a prime number.

ii. Neither 21 is a prime number nor it is divisible by 3.

iii. It is not true that 4+3i is a real number.

iv. 2 is the only even prime number and 5 divides 26.

v. Either 64 is a perfect square or 46 is a prime number.

vi. 3 + 5 > 7 if and only if 4 + 6 < 10.

Answer 1

i. Let p : 14 is a composite number,

q : 15 is a prime number.

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

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

\(\therefore\)truth value of p_q is T.

ii. Let p: 21 is a prime number,

q: 21 is divisible by 3.

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

~p^~q.

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

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

iii. Let p: 4 + 3i is a real number.

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

Since, truth value of p is F.

\(\therefore\)truth value of ~p is T.

iv. Let p: 2 is the only even prime number,

q: 5 divides 26.

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

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

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

v. Let p: 64 is a perfect square, 

q: 46 is a prime number.

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

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

\(\therefore\)truth value of p_q is T

vi. Let p: 3 + 5 > 7, q: 4 + 6 < 10

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

p\(\leftrightarrow\)q .

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

\(\therefore\)truth value of p\(\leftrightarrow\)q is F