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Four cards lie on table. Each card has a number printed on one side and a colour on the other. The faces visible on the cards are $2,3,$ red, and blue.

Proposition: If a card has an even value on one side, then its opposite face is red.

The card which MUST be turned over to verify the above proposition are

1. $2,$ red
2. $2,3,$ red
3. $2,$ blue
4. $2,$ red, blue
Migrated from GO Civil 3 years ago by Arjun

## 3 Answers

Best answer

If a card has an even value on one side, then its opposite face is red.

to verify this proposition:

• the card with even number must be turned to check whether the opposite face is red or not.
• If the face of the card is other then red colour, it's opposite face must not be even number, so this needs to be checked.
• If a card face is of red colour, the opposite side may contain any number, so checking this card is needless.
• If a card face contains an odd number, checking the opposite side colour is needless.

So, a card containing number $2$ on one side and colour Blue on opposite, needs to be turned to verify the proposition.

Hence, Option "C" is the correct choice.

For a statement to be true its contrapositive must also be true .

Let E= Number is even    R= Card is red

E –> R

For this even cards must be turned to check if the other side is Red because If E is true then R can’t be false . But we don’t care about the case where E is not true .

Contrapositive of E->R will be  R’->E’ (   ‘  is for negation)

For this non red cards must be turned to check if the other side should not be Even because If R’ is true then E’ can’t be false . But we don’t care about the case where R is true .

Truth table for →

### 1 comment

perfect logic bro
Need to check both Positive and Contrapositive of this statement:

If card face is even, then opposite is red. → Check even facing cards – 2

If face is not red, then opposite face is not even. → Checking cards whose face is not red – blue

Need to check cards blue and 2.
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