TTMUA Lab
TMUA 2019 · Paper 2 · Question 17 of 20

TMUA 2019 Paper 2 Question 17

Logic and arguments — Which option can be the unique correct one. Try it first; the answer and a full worked solution are below.

TMUA 2019 · Paper 2Logic and argumentsWhich option can be the unique correct one4 options
A multiple-choice test question offered the following four options relating to a certain statement:

A   The statement is true if and only if x > 1
B   The statement is true if x > 1
C   The statement is true if and only if x > 2
D   The statement is true if x > 2

Given that exactly one of these options was correct, which one was it?

  1. AA
  2. BB
  3. CC
  4. DD
Show the answer and worked solution
answer · D
  1. AA
  2. BB
  3. CC
  4. DD
Look at which options force others to be true as well. An "if and only if" is stronger than the matching "if", so if A were correct then B would be correct too, giving two correct options — so A is out, and the same argument rules out C because it would drag D along with it. Option B says x > 1 is enough for the statement, and since every x > 2 also satisfies x > 1, B correct would make D correct as well. That leaves D as the only option that can stand alone.