Q1. Find out DNF and CNF of the given identity without using the truth table:
(A → (B ∨ C)) → (A ∧ D)
Q2. State the DeMorgan’s laws. Prove it by using the truth table.
Q3. Check the validity of the given argument. If valid, make a formal proof, if not describe why.
‘If the labor market is perfect then the wages of all the persons in a particular employment will be equivalent. However it is always the case that wages for such persons are not equivalent thus the labor market is not perfect’.
a) Compute the number of distinct natural numbers not exceeding 1000 that are multiples of 10, 15, 35 or 55.
b) Illustrate that if R1 and R2 are equivalence relations on A, then R1∩ R2 is also in equivalence relation.