Name: SSN: Grade:MA334B EXAM 1 October 2001I pledge my honor that I have abided by the Stevens Honor System.1 (20pts)Let R, S, T be sets. Prove by using the element method or disprove by a exhibiting a counterexample.1. R ∪ (S ∩ T ) ⊆ (R ∪ S) ∩ (T ∪ S)2. S ∪ (R ∩ T ) ⊆ (R ∪ S) ∩ (T ∪ S)2 (20pts)Prove or disprove. An integer n is odd if and only if n2+ 4 is odd.3 (15pts)Use a truth table to check if the following is a tautology.(¬q → p) → (q → ¬p)4 (15pts)Let Σ = {a, b, c} be an alphabet. Let L1be the language consisting of all strings over Σ of length 5which begin with c and in which the letter a appears at least three times. Let L2be the languageconsisting of all palindromes (strings that read the same forward as backward) over Σ.1. List all elements of L1.2. Find L1− L2.5 (15pts)Let A = {x, y}, B = {1, 2, 3} and C = {a, b}.1. Partition BxC into 4 subsets.2. How large is the power set P (AxB)?6 (15pts)Prove by induction: ∀ n ≥ 1,nXi=112i = 6n2+