Discrete Mathematics

---------------------------SYMBOLIC

LOGIC

65

We could think

of

implication as cause and effect with the example "

If

Vasant drops an egg, it will

crack". The contrapositive says,

"If

the egg did not crack, then Vasant did not drop it". After all,

if

Vasant had

dropped it, then it should have cracked. Now, consider the converse.

"If

the egg is cracked, then Vasant

dropped it." Not necessarily so. Vasant could have hit it,

or

crushed it. There may be multiple causes to the

same effect (cracking

of

the egg).

The inverse says,

if

Vasant did not drop an egg, then

it

did not crack. Again, this is

not

so, because the

egg could have been cracked even ...