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7 votes

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

- $2,$ red
- $2,3,$ red
- $2,$ blue
- $2,$ red, blue

7 votes

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.

2 votes

**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 .

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