Let Qx y be the statement x y x y If the domain for both

Let Q(x, y) be the statement x + y = x ? y. If the domain for both variables consists of all integers, what are the truth values?

a) Q(1, 1)

b) Q(2, 0)

c) ?yQ(1, y)

d) ?xQ(x, 2)

e) ?x?yQ(x, y)

f) ?x?yQ(x, y)

g) ?y?xQ(x, y)

h) ?y?xQ(x, y)

i) ?x?yQ(x, y)

We are given statement

x+y=x-y

(A)

Q(1,1)

we plug x=1 and y=1

we get

1+1=1-1

they can not be equal

so, it is false

(B)

Q(2,0)

we plug x=2 and y=0

and we get

2+0=2-0

2=2

so, this is true......Answer

(C)

y Q(1, y)

we can plug that in statement

we get

1+y=1-y

We can get equality

1=1

Hence , this is true........Answer

(D)

x Q(x, 2)

we can plug values in statment

and we get

x+2=x-2

2=-2

so, it is false.......Answer