Exercise 1.5 (2)

Ex. 2:  If B = {2, 3, 5, 6, 7} determine the truth value of each of the following.
i) ∀ x ∈ B such that x is prime number.
Ans:  
For x=6, x is not a prime number.
∴ x=6 does not satisfies the given statement.
∴ The given statement is false.
∴ It’s truth value is F.

ii) ∃ n ∈ B, such that n + 6 > 12
Ans: 
For n=7, n+6=7+6=13 >12.
∴n=7 satisfies the equation n+6 >12.
∴ The given statement is true.
∴ It’s truth value is T.

iii) ∃ n ∈ B, such that 2n + 2 < 4
Ans: 
There is no n in B which satisfies 2n+2<4.
∴ The given statement is false.
∴ It’s truth value is F.

iv) ∀ y ∈ B such that y2 is negative
Ans: 
There is no y in B which satisfies y^2<0.
∴ The given statement is false.
∴ It’s truth value is F.

v) ∀ y ∈ B such that (y − 5) ∈ N
Ans: 
For y = 2,  y – 5 = 2 – 5 = -3 ∉ N.
∴ y = 2 does not satisfies the equation (y – 5) ∈ N.
∴ The given Statement is false.
∴ It’s truth value is F.