The text editor for this blog doesn't have any arrow symbol, either for mapping or for implication. Instead, the mapping arrow will be written as -> and the implication arrow will be =>.

For all these problems, let p = 1100 and q = 1010. Determine if the following logical statements are tautologies (all 1's), contradictions (all 0's) or conditional (some 1's and some 0's).

Problem 1.

(p v q) => ~p

Problem 2.

p v (q => ~p)

Problem 3.

(p ^ q) => ~p

Problem 4.

(p ^ ~p) => q

Answers in the comments.

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## 1 comment:

Problem 1.

(p v q) => ~p

1100 v 1010 = 1110

Change implication to ~premise v conclusion.

~1110 = 0001

0001 v 0011 =

0011.This statement is conditional.

(Thanks to Phillip Barringer for the correction.)

Problem 2.

p v (q => ~p)

q => ~p becomes ~q v ~p

0101 v 0011 = 0111

1100 v 0111 =

1111.This statement is a tautology.

(This one also needed to be corrected.)

Problem 3.

(p ^ q) => ~p

p ^ q = 1100 ^ 1010 = 1000

~1000 = 0111

0111 v 0011 =

0111.This statement is conditional.

Problem 4.

(p ^ ~p) => q

p ^ ~p = 1100 ^ 0011 = 0000

~0000 = 1111

1111 v 1010 =

1111.This statement is a tautology. (Any implication where the premise is a contradiction will be a tautology.)

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