Answer to Question #233066 in Discrete Mathematics for shab

Question

Let Q(x) be the statement “x + 1 > 2x.” If the domain consists of all integers, what are these truth values? a) Q(0) b) Q(−1) c) Q(1) d) ∃xQ(x) e) ∀xQ(x) f) ∃x¬Q(x) g) ∀x¬Q(x)

Answer 1

QUESTION

Let Q(x) be the statement “x + 1 > 2x.” If the domain consists of all integers, what are these truth values? a) Q(0) b) Q(−1) c) Q(1) d) ∃xQ(x) e) ∀xQ(x) f) ∃x¬Q(x) g) ∀x¬Q(x)

SOLUTION

a) Q(0) is true because;

put x = 0 in x + 1 > 2x

= 0 + 1 > 2 * 0

= 1 > 0

Answer: True

b) Q(-1) is true because;

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

= - 1 + 1 > 2 (-1)

= 0 > -2

Answer: True

c) Q(1) is false because;

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

= 1 + 1 > 2 * 1

= 2 > 2

But this is not true

Answer: False

d) the statement is true because;

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

= 0 + 1 > 2 * 0

= 1 > 0

Answer: True

e) The statement is false because;

When we put x = 1 then statement becomes false.

Answer: False

f) The statement is true because;

If x = 3

3 + 1 ≤ 2 * 3

= 4 ≤ 6

So the statement is true

Answer: True

g) The statement is false because

If we suppose x = 0 and x + 1 ≤ 2x

then,

0 + 1 ≤ 2 * 0

= 1 ≤ 0

Answer: False