Answer to Question #164149 in Discrete Mathematics for Abdi Endebu

Question

Q(X,y):X+y >or=7 then what is truth value of∀x∃yQ(x,y)

Answer 1

 The answer depends on the set where the values of x, y are defined. Given ,

$Q(x,y):x+y\ge7$

$\forall x \exist yQ(x, y)$

For all value of x Let x=1 and y=1:

$$x+y=1+1=2<7$$ $$2\text{ is less than }7$$

Since $x+y\le7$ The truth value of Q is false for some values of x and y.

$\text{At } x=8,y=2\\ X+y=8+2=10>7$

then the truth value of Q(x, y) is true for some values of x and y