Let S and T be disjoint sets. Show that P(S) X P(T) and P(S U T) have the same cardinality two ways.

(a) Using the formulae for set cardinality

(b) Directly by showing there is a bijection between them. (you must prove that your function is a bijection

S and T are 2 disjoint sets

so P(S)constains 2^n elements

and P(T) contains 2^p elements

so,P(S)*P(T)=2^n+p

P(SUT)=2^n+2^p (for disjoint set)

Secure Information

Content will be erased after question is completed.

Enter the email address associated with your account, and we will email you a link to reset your password.

Forgot your password?

Sign Up