In the following, p,q, and denote propositions. Recall that ~ denotes negation,

Question

In the following, p,q, and denote propositions. Recall that ~ denotes negation, conjunction, v disjunction,-implication,biconditional Construct a truth table for (p V q) (p ^-q). Find a simpler proposition that is logically equivalent to (pvg)(p^~q), the expression from exercise 1. Use a truth table to show that p q and ~pv q are logically equivalent. Write the negation to "if it is raining then it is cloudy" that is in the form of a conjunction. show that p p is a tautology. Determine whether p ~p is a tautology, a contradiction, or neither. DeMorgan's laws: 1. 2 3. 4. 5, 6. 7. a. Show that (p V q) and (-p)ACq) are logically equivalent b. Show that ~ (p q) and (-pjv (-q) are logically equivalent 8. Show that ((p q) ^ (q r)) (p r) is a tautology.

Explanation / Answer

Q1

p q (pVq) ~q (p~q) (pVq)--> (p~q)

T T T F F F

T F T T T T

F T T F F F

F F F T F T

Q2. from the above truth table we can say that

(pVq)---->(p^~q) is equivalent to ~q

Q.3

p q p-->q ~p ~pVq

T T T F T

T F F F F

F T T T T

F F T T T

from above truth table p-->q and ~pVq are equivalent

Q4.if it is not raining then it is not cloudy.

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