Question

Q.3. The logical operator "" is read "if and only if". PQ is defined as being equivalent to (P→Q) ˄ (Q→P). Based on this definition, show that PQ is logically equivalent to (P˅Q) → (P˄Q): a. by using truth tables.

Q.4. Prove that implication is transitive in the propositional calculus, that is, that ((P→Q) ˄(Q→R)) → (P→R))

Answer 1

what does ˄ and ˅ mean ?? 'and' and 'or'

Answer 2

and i guess -> means implies ... right??

Answer 3

right

Answer 4

P Q P&Q
0 0 0
0 1 0
1 0 0
1 1 1

since P <-> Q

P Q P'or'Q
0 0 0
0 1 0 (one of them implies other so it must be false.)
1 0 0
1 1 1

Answer 5

this is the ans. of Q.3 ?

Answer 6

i guess so ... though not so i am not so sure!!!

Answer 7

P Q R P->Q Q->R (P->R^Q->R) P->R
0 0 0 1 1 1 1
0 0 1 1 1 1 1
0 1 0 1 0 0 1
0 1 1 1 1 1 1
1 0 0 0 1 0 0
1 0 1 1 0 0 1
1 1 0 1 0 0 0
1 1 1 1 1 1 1

must be something like this ....