GATE ECE 2017 Set 2 | GA | Question: 3

Question

A rule states that in order to drink beer, one must be over $18$ years old. In a bar, there are $4$ people. $P$ is $16$ years old. $Q$ is $25$ years old. $R$ is drinking milkshake and $S$ is drinking a beer. What must be checked to ensure that the rule is being followed?

• A. Only $\text{P’s}$  drink
• B. Only $\text{P’s}$  drink and $\text{S’s}$ age
• C. Only $\text{S’s}$ age
• D. Only $\text{P’s}$  drink, $\text{Q’s}$ drink and $\text{S’s}$ age

Comments

i generally solve these types of questions using propositional logic.

We are given that:  If a person drinks beer, then Age must $>18$. this is simple $A\rightarrow B$

Implication is false only for once case when $A=True$ and $B=False$. So we will check for this case.

1. For $P$

Since Age $<18$ therefore $b=false$ here, this can lead to breakage of rule ,
hence we need to check the value of $A$ i.e. what he is drinking ?

2. For $Q$

Age $>18$ therefore $A\rightarrow B$ can never be false coz $B=true$. Hence no need to check.

3. For $R$

$R$ is drinking a milkshake thereforce, $A=false$ here. Hence no need to check

4. For $S$

since $S$ is drinking beer thererfor $A=true$, we will need to check for the age of $S$ to know if age $>18$ and consecutively value of $B$ will be determined.

Answer 1

• If a person drinking beer, his age should be checked, to verify he's eligible (>18 years old)
• If a person not drinking beer, checking him is useless.
• If a person is younger than 18 years old, his drink must be checked, It should not be beer.
• If a person is older than 18 years old, checking his drink is useless.

So, here Only $P’s$ drink and $S’s$ age should be checked to ensure that the rule is being followed.
Correct Answer: $B$

Answer 2

In this question the rule states that "in order to drink beer the person must be over 18 years of age". So we will consider the following options according to the rule:

For P it is given that his/her age is 16 years and since he/she is below 18 years of age, they cannot have beer so we have to check P's drink to see if the rule is followed.

For Q it is given that his/her age is 25 years and the rule states nothing about what anyone above 18 years cannot drink therefore there is no restriction on him/her. We do not need to check his/her drink.

For R it is given that he/she is having a milkshake. Now for milkshake also the rule puts no restriction therefore there is no need to check his/her age.

and finally for S it is given that he/she is having a beer and now since the rule clearly states that if anyone is having beer then he/she must be over 18 years of age therefore we need to check S's age.

So the correct option is Option B) We need to check P's drink and S's age

Comments

But, P is not drinking anything, right?

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@chauhansunil20th not from the question but from the options we can say P is drinking.

Answer 3

For a statement to be true both its implication and its contrapositive must be true .
Implication:- If a person is having beer then he must be 18+ of age.(S’s age)

contrapositive :- if a person is not 18+ then he cannot have beer.(P’s drink).