Question

2. (a) Consider the statement ducks quack If all chickens lay eggs then some Write down in words the (i) conversE (ii) contrapositive (b) Now consider the statement For every tree on the Barr Smith Lawns there is a leaf tree that did not fall off last autumn on that Write down (in words) the negation of this statement

Answer 1

(a)

(i)

Statement: If all chickens lay eggs then some ducks quack

Converse:If some ducks quack then all chickens lay eggs.

Explaination: Converse of statement is the opposite of the scenerio inside the statement.Hence, "If all chickens lay eggs then some ducks quack" becomes "If some ducks quack then all chickens lay eggs".

(ii)

Statement: If all chickens lay eggs then some ducks quack

Contrapositive : If some ducks did not quack then all chickens does not lay eggs.

Explaination: Contrapositive of statement is the opposite and negative of the scenerio inside the statement.Hence, "If all chickens lay eggs then some ducks quack" becomes "If some ducks did not quack then all chickens does not lay eggs".

b)

Statement: For every tree on the Barr Smith Lawns there is a leaf on that tree that did not fall off last autumn.

negation :For every tree on the Barr Smith Lawns there is no leaf on that tree that will fall off last autumn.

Explaination: This is usually referred to as "negating" a statement. if a statement is true, then its negation is false and if a statement is false, then its negation is true.