Exercise 1.5 (1)

Ex. 1: Use quantifiers to convert each of the following open sentences defined on N, into a true statement.
i) x2 + 3x − 10 = 0
Ans: 
∃ x ∈N, Such that x^2+3x -10=0 
It is true statement, since x=2 ∈ N  Satisfies it.

ii) 3x − 4 < 9
Ans: 
∃ x ∈N, Such that 3x -4 <9
It is true statement, since x=1,2,3,4 ∈N  Satisfies 3x -4 <9

iii) n2 ≥ 1
Ans: 
∀ n ∈N, n^2  ≥1
It is true statement, since all n ∈N satisfy n^2≥1

iv) 2n − 1 = 5
Ans: 
∃ n ∈N, Such that 2n -1=5
It is true statement, since n = 3 ∈ N satisfy 2n -1=5

v) Y + 4 > 6
Ans: 
∃ y ∈N, Such that y+4>6
It is true statement, since y = 3,4,…∈ N satisfy  y+4 >6

vi) 3y − 2 ≤ 9
Ans: 
∃ y ∈ N, Such that 3y – 2 ≤ 9 
It is true statement, since y = 1,2,3 ∈ N satisfy 3y -2 ≤9