Question

Use quanlifiers to convert each of the following open sentences defined on N, into a true statement:

(i) $x+5=8$ (ii) $x^2>0$ (iii) $x+2<4$

Answer 1

(i) $\exists x\in N$ such that $x+5=8$ is a true statement, since, $x=3\in N$ satisfies $x+5=8.$

(ii) $x^2>0\forall x\in N$ is a true statement, since the square of every natural number is positive.

(iii) $\exists x\in N$ such that $x+2<4$ is a true statement, since $x=1\in N$ Satisfies $x+2<4.$