Es) Using truth tables, show that pay and (p → r) ^ (q → r) are not logically equivalem

equation (after factoring) is (x+3)²(x − 2)²(x − 6) = 0. Justify your answer. (b) Consider the sequence defined by the recurrence: An 3An-1-4An-3 with initial conditions Ao = 1, A₁ = -2 and A₂ = 0. Give the values of A4 and A5. Show your work. =

R ⋈ (S ∩ T) = (R ⋈ S) ∩ (R ⋈ T)   Show if this relational algebra is equal or not with proof.

Show that each argument is not valid by finding a truth assignment of the variables that makes the hypotheses true, but the conclusion false. (Hint: fill out a truth table if you have trouble finding an assignment.) PVr (a) P^r

Logical equivalence of the given proposition:   p if and only if q      and       (p→g) ^ (q→p)

Q2. What is the Master Theorem? What kind of the problems are solved through this theorem. Use Master Theorem to give the tight asymptotic bounds of the following recurrence relation. T (n) = 2T (n/2) + n²

Use a proof by cases to show that min(a, min(b, c)) = min(min(a, b), c) when b ≥ a ≥ c.