For each of the following compound statements, first identify the
corresponding component statements. Then check whether the statements are
true or not.
(i) If a triangle ABC is equilateral, then it is isosceles.
(ii) If
a
and
b
are integers, then
ab
is a rational number

Question

For each of the following compound statements, first identify the
corresponding component statements. Then check whether the statements are
true or not.
(i) If a triangle ABC is equilateral, then it is isosceles.
(ii) If
a
and
b
are integers, then
ab
is a rational number

terenzreignz · Answer

Component statements are just the pieces of the compound statements...
In this case
If P then Q
the components are P and Q.
If P is false, then regardless of the truth-value of Q, the conditional "if P then Q" statement is true.
If P is true and Q is true, then the conditional "if P then Q" statement is true.

Finally, if P is true and Q is false, then the conditional "if P then Q" statement is false.