a. Use a truth table to show that -pv q and q -p are equivalent b. Use the resul

Question

a. Use a truth table to show that -pv q and q -p are equivalent b. Use the result from part (a) to write a statement that is equivalent to the statement below. The sun is not out or it is not night. a. Use the given truth values for p and q to determine the truth values for the other statements b. Which statement below is equivalent to the given stalement? A. If it is night then the sun is not out B. The sun is out or it is not night O C. If it is not night then the sun is out D. The sun is not out or it is night

Explanation / Answer

1. a.

As the last two columns show identical values,

~pv~q and q->~p are equivalent.

b. Let p:The sun is out q:it is night

Given statement "The sun is not out r it is not night" is ~pv~q

By the proven equivalence, this is same as q->~p

which translates to:

If it is night then the sun is not out

2. a. Note: This is identical to the earlier table. Rewriting:

b. As proven earlier, the equivalent statement is

If it is night then the sun is not out

3.

As seen by the values of the final column, the statement is neither a tautology nor a self-contradiction.

p q ~p ~q ~pv~q q->~p T T F F F F T F F T T T F T T F T T F F T T T T

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