If all students are boys and all boys are dancers, then which one of the following statements is definitely true?
All dancers are boys
All boys are students
All dancers are students
All students are dancers
Answer is Right!
Answer is Wrong!
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.