Question

Which statement completes the syllogism?

a. If |x| < a for some positive number a, then x < a.

b.

c. If |x| < a for some positive number a, then x > –a.

Question 3 options:

A) If |x| < a for some positive number a, then x < a.

B) If |x| < a for some positive number a, then x > –a.

C) If x < a then x > –a.

D) If x > –a then x < a.

Answer 1

Option C is correct i.e., if x < a then x > -a.

Explanation:

if |x| < a for some positive number a,

then by solving the inequality,

we get, -a < x < a .....(1)

i.e., x lies between -a and a.

from equation (1),if x < a then x > -a (which should be statement b)

So, we can say that If |x| < a for some positive number a, then x < a and x > –a (which is statement a and c).

so, the correct option is C i.e., if x < a then x > -a.