Examine the following statements:
Which one of the following conclusions is valid in the context of the above statements?
To determine the valid conclusion, let's analyze each statement using conditional logic:
If I am not bored, I do not watch TV.
This conclusion is the contrapositive of Statement 1. A contrapositive statement is logically equivalent to the original conditional statement. Since Statement 1 (P → Q) is given as true, its contrapositive (¬Q → ¬P) must also be true. Therefore, "If I am not bored, then I do not watch TV" is a valid deduction.
This is the converse of Statement 1 (Q → P). Statement 1 (P → Q) establishes that watching TV implies boredom, but it does not assert that boredom necessarily leads to watching TV. The converse of a true statement is not always true.
From Statement 2 (R → ¬Q), its contrapositive is (Q → ¬R), meaning "If I am bored, then I do not have my brother's company." Option (B) suggests the opposite (Q → R), which directly contradicts the logical inference from Statement 2. Therefore, this conclusion is invalid.
From Statement 2 (R → ¬Q), its contrapositive is (¬R → Q), meaning "If I am not with my brother, then I am bored." However, as established for Option (A), being bored (Q) does not necessarily imply watching TV (P) according to Statement 1 (P → Q). Therefore, this conclusion cannot be validly drawn.