You haw .seen how to generate compound statements using the four connectives , a

Question

You haw .seen how to generate compound statements using the four connectives , and, This problem addresses the question whether all four connective are necessary. Use a truth table to show that. A B is equivalent to (A and B). Show that A and B can be written using, only the connectives and. Thus the two connectives and suffice to generate all compound statements. It is possible to further reduce to only one connective, albeit a different one: Let us define the new connective NOR by setting A NOR B (A and B). Show that the four compound statements A, A and B, A or B and A B can be written using only the NOR-connective.

Explanation / Answer

A B ~B An~B ~(An~B) A=>B

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T T F F T T

T F T T F F

F T F T F F

F F T F T T

THE TRUTH VALUES OF A=>B AND ~(An~B) ARE SAME.THEREFORE THEY ARE EQUIVALENT.

A V B can be written as ~(~A n ~B)

A B ~A ~B ~(~An~B) AVB

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T T F F T T

T F F T T T

F T T F T T

F F T T F F

the truth values of (A v B) and ~(~A n ~B) are same

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