If p then q is represented as p -> q Negation of "if p then q" is represented as ~(p -> q)
what is the correct truth table for p V~ q
A+
p --> q and q --> p are not equivalent p --> q and q --> (not)p are equivalent The truth table shows this. pq p --> q q -->(not)p f f t t f t t t t f f f t t t t
The truth values.
Construct a truth table for ~q (p q)
If p then q is represented as p -> q Negation of "if p then q" is represented as ~(p -> q)
what is the correct truth table for p V~ q
P | T T F F Q | T F T F Q' | F T F T P + Q' | F T F F The layout is the best I could do with this software. Hope it is OK.
A+
. p . . . . . q. 0 . . . . . 1. 1 . . . . . 0
Not sure I can do a table here but: P True, Q True then P -> Q True P True, Q False then P -> Q False P False, Q True then P -> Q True P False, Q False then P -> Q True It is the same as not(P) OR Q
1)p->q 2)not p or q 3)p 4)not p and p or q 5)contrudiction or q 6)q
No, the inverse is not the negation of the converse. Actually, that is contrapositive you are referring to. The inverse is the negation of the conditional statement. For instance:P → Q~P → ~Q where ~ is the negation symbol of the sentence symbols.
"if p then q" is denoted as p → q. ~p denotes negation of p. So inverse of above statement is ~p → ~q, and contrapositive is ~q →~p. ˄ denotes 'and' ˅ denotes 'or'
P . . Q . . (P or Q)0 . . 0 . . . 00 . . 1 . . . 11 . . 0 . . . 11 . . 1 . . . 1=================P . . Q . . NOT(P and Q)0 . . 0 . . . . 10 . . 1 . . . . 11 . . 0 . . . . 11 . . 1 . . . . 0
p --> q and q --> p are not equivalent p --> q and q --> (not)p are equivalent The truth table shows this. pq p --> q q -->(not)p f f t t f t t t t f f f t t t t