NIMCET 2011 Logical Reasoning Question 85 with Solution

Question 85

Logical Reasoning Syllogism Easy

A causes B or C, but not both
F occurs only if B occurs
D occurs if B or C occurs
E occurs only if \( C \) occurs
J occurs only if E or F occurs
D causes G or H or both
H occurs if E occurs
\( G \) occurs if \( F \) occurs

If \( J \) occurs, which must have occurred ?

(A) Both \( E \) and \( F \)

(B) Either B or C

(C) Both B and C

(D) None of these

View Dynamic Solution & Explanation ▼

Correct Solution: Option B

Step-by-step Solution:

To solve the syllogism, we need to trace back the conditions that must be true for J to occur.

Analyzing the Conditions

Condition for J: J occurs only if E or F occurs. This means if J happens, we know for certain that either E or F (or both) must have happened first.
Condition for E: E occurs only if C occurs. So, if we know E happened, we also know C must have happened.
Condition for F: F occurs only if B occurs. So, if we know F happened, we also know B must have happened.
Initial Condition: A causes B or C, but not both. This sets up the initial chain of events.
(Note: The statements about H and G are consequences of E and F, but not requirements for them, so they aren't needed to solve the problem.)

Tracing the Logic Backwards from J

Since we know J occurred, we have two possible paths that could have led to it:

Path 1: J occurred because E occurred. Since E only occurs if C occurs, this path requires that C must have occurred.
Path 2: J occurred because F occurred. Since F only occurs if B occurs, this path requires that B must have occurred.

Therefore, for J to have occurred, one of these two paths must have been taken. This means that either B or C must have occurred.

The final answer is: B or C