Paper2

Question 1

A if B

Answer 1

If B occurs then A must occur
(A can occur without B occurring)

Question 2

A only if B

Answer 2

If A occurs then B must also occur
(B can occur without A occurring)

Question 3

A if and only if B

Answer 3

If A occurs then B occurs and if B occurs then A must also occur

Question 4

Necessary

Answer 4

It is required for something to happen. For example it is necessary to be a quadrilateral to be a square but it isn’t sufficient

Question 5

Sufficient

Answer 5

It is adequate for something to happen, it is sufficient to be a square in order or be a quadrilateral but it isn’t necessary

Question 6

All A are B (negation)

Answer 6

Some A are not B

Question 7

No A are B (negation)

Answer 7

Some A are B

Question 8

Some A are B (negation)

Answer 8

All A are not B or None of A are B

Question 9

Converse of a statement

Answer 9

When the hypothesis and conclusion are swapped so If A then B would become If B then A.

Question 10

Contrapositive of a statement

Answer 10

If the converse negation of a statement so if A then B would become If not B, then not A

Question 11

Remainder Theorum

Answer 11

If f(a) = k, then f(x-a) leaves a remainder k when dividing f(x). So f(x)=(x-a)g(x)+k