Question

Which of the following is a compound proposition? \[ \text{A. Unless it rains in time, harvest will not be good.} \] \[ \text{B. Only meritorious students will be considered for scholarship.} \] \[ \text{C. Be neither a borrower nor a lender.} \] \[ \text{D. Two triangles are formed if a square is divided diagonally.} \] \[ \text{E. Not all good speakers are good writers.} \]

• A. A, B and C only
• B. A, C and D only
• C. B, C and D only
• D. B, D and E only

Hint:

Words like “unless”, “if”, and “neither...nor” usually indicate compound propositions.

Answer 1

The Correct Option is B

Concept:
A compound proposition is a proposition formed by combining two or more simple propositions with logical connectives such as: \[ \text{and, or, if...then, unless, neither...nor} \] A simple proposition contains only one basic assertion.

Step 1: Check statement A.
Statement A is: \[ \text{Unless it rains in time, harvest will not be good.} \] The word unless expresses a conditional relation. It can be understood as: \[ \text{If it does not rain in time, then harvest will not be good.} \] So, A is a compound proposition. \[ A = \text{Correct} \]

Step 2: Check statement B.
Statement B is: \[ \text{Only meritorious students will be considered for scholarship.} \] This is a simple categorical-type statement. It does not combine two propositions by a logical connective. So, B is not selected.

Step 3: Check statement C.
Statement C is: \[ \text{Be neither a borrower nor a lender.} \] The expression neither...nor combines two negative ideas. It means: \[ \text{Do not be a borrower and do not be a lender.} \] So, C is a compound proposition. \[ C = \text{Correct} \]

Step 4: Check statement D.
Statement D is: \[ \text{Two triangles are formed if a square is divided diagonally.} \] The word if makes it a conditional proposition. It means: \[ \text{If a square is divided diagonally, then two triangles are formed.} \] So, D is also a compound proposition. \[ D = \text{Correct} \]

Step 5: Check statement E.
Statement E is: \[ \text{Not all good speakers are good writers.} \] This is a quantified negative statement. It does not combine two separate propositions by a connective. So, E is not selected.

Step 6: Final conclusion.
The compound propositions are: \[ A,\ C,\ D \] Hence: \[ \boxed{\text{(B) A, C and D only}} \]