Would anyone be so kind and be able to help me with this?

Question

Use a truth table to represent the statement, "If x² ≤ 100, then x ≤ 10."

I have been struggling with this question for a while now, could someone please help me understand this?

Also, thank you in advance for helping me and answering this. ♥

Answer 1

A is the statement that x^2<=100

B is the statement that x<=10

If A then B

Or A->B

A. B. a->B

T. T. T

T. F. F

F. T. T

F. F. T

Answer 2

x² ≤ 100

x ≤ 10 ← this inequality was derived from the 1-st one by taking square roots from left and right sides.

Note that this operation does not change the relationship in the 2-nd inequality, i.e. the sign of inequality is the same.

It is useful to remember that multiplication or division by a negative number will change the sign of the inequality and this was not the case here.