Prove that (((p v ~q) ⊕ p) v ~p) ⊕ (p v ~q) ⊕ (p ⊕ q) is
equivalent to p ^ q. Please show your work and name all the logical
equivalence laws for each step. ( v = or, ~ = not, ⊕ = XOR)
Thank you
Suppose a is a positive integer and p is a prime/ Prove that p|a
if and only if the prime factorization of a contains p.
Can someone please show a full proof to this, thank you.
A
biased coin (P(head) = p , p is not equal to 0.5) is tossed
repeatedly. Find the probability that there is a run of r heads in
a row before there is a run of s tails, where r and s are positive
integers. Express the answer in terms of p, r and s.