Discrete Mathematics

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43

EXERCISE

2 Give a direct proof that

if

x and y are odd integers then x + y is even.

EXERCISE

3 Show that any integer composed

of

3"

identical digits is divisible by

3".

EXERCISE

4 Mr. Kapur claims that he is one-third Indian. When asked how this is possible, his answer was,

'My father was one-third Indian and my mother was one-third Indian.' Is this a correct proof by induction?

EXERCISE

5 The king summoned the best mathematicians in the kingdom to the palace to find out how

smart they were. The king told them,

'I

have placed white hats on some

of

you and black hats