If all students are boys and all boys are dancers, then which one of the following statements is definitely true?
[amp_mcq option1=”All dancers are boys” option2=”All boys are students” option3=”All dancers are students” option4=”All students are dancers” correct=”option4″]
This question was previously asked in
UPSC CAPF – 2017
1. All students are boys. (If someone is a student, then that person is a boy. Student -> Boy)
2. All boys are dancers. (If someone is a boy, then that person is a dancer. Boy -> Dancer)
We can combine these two conditional statements using the principle of transitivity:
If Student -> Boy and Boy -> Dancer, then it logically follows that Student -> Dancer.
This means, “If someone is a student, then that person is a dancer,” which can be rephrased as “All students are dancers.”
Let’s examine the options based on this deduction:
A) All dancers are boys (Dancer -> Boy). This is the converse of “All boys are dancers” and is not necessarily true.
B) All boys are students (Boy -> Student). This is the converse of “All students are boys” and is not necessarily true.
C) All dancers are students (Dancer -> Student). This is the converse of the derived conclusion “All students are dancers” and is not necessarily true.
D) All students are dancers (Student -> Dancer). This is the direct logical conclusion derived from the premises.