(1) Is p→ (q V r) logically equivalent to → (p Vr)? Prove your answer.

Q: Prove that (C, +) ≈ (R × R, +).

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Q: If  A  is singular then det(A)=0 true or false

A: If  A  is singular then det(A)=0. We have to state true or false for this statement.

Q: |u| = |v| show that (u + v) • (v - u) = 0 is logically equivalent to condition u⚫u=v•v

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Q: 21 -2 T 5. If B= 1 -2 T = - +4 = 2 +5 1 Using two methods to find [T]B-

A: Method I- Let T be linear transformation on  a Vector space V with n dimension with basis…

Q: Let n be a positive integer and let u(x, y) = (x² + y²)". Show that (2²2²2 + 3²²) ₁ dx² дуг u(x, y)…

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Q: [x +1 0 2 1 2 (3)if A = 3 1 and B = 3 y -5 4 -1 -5 4 z - 4. Find x,у аnd z.

A: If two matrix A and B are equal then Each matrix of A and B has the same number of rows. Each matrix…

Q: Proof by contrapositive that for xy EZ, if xy is even then either x or y is even.

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Q: (3x)[R(x) V S(x)]→(3x)R(x) V (3x)S(x)

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Q: Let f(x)= x+1, find all xeR such that f[f(x)]=2 the solution set is: а. у%3D0. b. y=x. с. у#х. d.…

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Q: Reason ер Vx(P(x)v Q(x)) P(a)vQ(a) P(a)vQ(a)v R(a) Premise Vx(-P(x)^Q(x))→R(x)) (-P(a)^Q(a))→R(a)…

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Q: k – 1 k+1 Let h : Z → Q × Q, given by h(k) : 2 2 Let G = {(m, m +1) | m E Z}. Show that G C h(Z).

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