Answer:
~ is for negation
^ is for "and"
v is for "or"
=> for "if then"
<=> for "if and only if"
Step-by-step explanation:
(a) ~P (negation of P)
I didn't buy a lottery ticket this weekend.
(b) P v Q (P is in disjunction Q)
I have either bought a lottery ticket this weekend or won the million dollar jackpot.
(c) P => Q (Q is a consequence of P)
I won the million dollar jackpot because I bought a lottery ticket this weekend.
(d) P ^ Q (P is in conjunction with Q)
I bought a lottery ticket this weekend, and I won the million dollar jackpot.
(e) P <=> Q (P and Q are dependent on each other)
If only I had bought a lottery ticket this weekend, I would have won the million dollar jackpot.
(f) ~P => ~Q (negation of Q is a consequence of negation of P)
I didn't win the million dollar jackpot because I didn't buy a lottery ticket this weekend.
(g) ~P ^ ~Q (negation of P is in conjunction with negation of Q)
I neither bought a lottery ticket this weekend nor won the million dollar jackpot.
(h) ~P v (P ^ Q)
This is logically equivalent to (~P v P) ^ (~P v Q) (negation of P is in disjunction with P, and also with disjunction with Q), and can be best expressed as:
It didn't matter that I bought a jackpot ticket or not, I won the million dollar jackpot.
