# If Gloria performs first, which one of the following could be true?

Sabrina on December 4, 2019

Explanation

Can I see a setup for this game please

Replies

Irina on December 4, 2019

@Sabrinamc,

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.

on January 27, 2021

i know where my problem lies thank you.