The game requires us to determine the order of performances for five students - G H R S T
__ __ __ __ __ 1 2 3 4 5
The following rules apply:
(1) H must perform earlier than R.
H > R
This rule allows us to infer that R cannot perform first and H cannot perform 5th. __ __ __ __ __ 1 2 3 4 5 ~R ~H
(2) If G performs earlier than T, then R &S must also perform earlier than T.
G > T -> R & S > T
This rule tells us that if G performs earlier than T, then T must be #5 because all four other students must perform before
G > H > R > T S >
The contrapositive of this rule is:
T > R v S -> T > G
If either R or S performs later than T, we can conclude that G must also perform later than T.
(3) H must perform earlier than both S & T or else later than both of them.
H > S & T v S &T < H
resulting in the following chains:
H > R > S & T
or S & T > H > R
The question asks us if G performs first, which of the following could be true?
If G performs first, then per rule (2), R & S must also perform before T, and we know that T must be fifth per our inference above, hence we can eliminate (C) and (E). H must perform before R per rule 1, hence we can eliminate (B). Per rule 3, H must perform earlier than S & T, hence H must be #2 - eliminate (A). (D) - S performs third is the only scenario that could be true, resulting in the following order:
G H S R T
Let me know if this makes sense and if you have any other questions.
on January 27, 2021
i do have a question? i believe youre deduction is wrong? when G is first T is fourth not fifth. if you put T fifth than H would be in the middle of R and T which is against the rules. if i am wrong correct me.
