Question

Let Q(x) be the statement "x +1 2x." If the domain consists of all integers, what are these truth values?

Answer 1

Answer:

a) True

b) True

c) False

d) True

e) False

f) True

g) False

Step-by-step explanation:

a) Q(0) is true because;

put x= 0 in x+1>2x

==> 0+1>2×0

==> 1>0

b) Q(-1) is true because;

if we put x= -1 in x+1>2x

==> -1+1>2 (-1)

==> 0> -2

c) Q(1) is false because;

if we put x=1 in x+1>2x

==> 1+1> 2 ×1

==> 2>2

which is not true!

d) the statement is true because;

If we put x=0 in x+1>2x

==> 0+1>2×0

==> 1>0

e) The statement is false because;

if we put x=1 then statement becomes false as well !

f) The statement is true because;

If x=3

3+1≤2×3

==> 4≤6

So our statement is true

g)  The statement is false because

If we suppose x=0 and x+1≤2x

then,

0+1≤2×0

==> 1≤0

Which is false - so x+1≥2x is true