a Delta B
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This document discusses a math problem involving sets. It asks to prove that A Δ B = (A - B) U (B - A), where A = {1, 2, 3, 4, 5} and B = {3, 4, 5, 6, 7}. It shows the step-by-step working, finding the elements of A Δ B, A - B, and B - A, and demonstrating they are equal, proving the original statement.
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a Delta B
- 1. ONLINE CLASS OF MATHEMATICS FOR IX CLASS TEACHER : SIR AHSAN TOPIC : SET
- 2. Q1: If A = {1, 2, 3, 4, 5} & B = {3, 4, 5, 6, 7} Prove that A Δ B = (A – B) U (B – A)
- 3. Solution: A Δ B = (A – B) U (B – A) Taking L.H.S A Δ B = {1, 2, 3, 4, 5} Δ {, 3, 4, 5, 6, 7} A Δ B = {1, 2, 6, 7}
- 4. Taking R.H.S (A – B) U (B – A) First we find (A – B) A – B = {1, 2, 3, 4, 5} – {3, 4, 5, 6, 7} A – B = { 1, 2 } Than find (B – A) B – A = {2, 3, 4, 5, 6, 7} - {1, 2, 3, 4, 5} B – A = {6, 7}
- 5. Now, (A – B) U (B – A) (A – B) U (B – A) = { 1, 2 } U { 6, 7 } (A – B) U (B – A) = {1, 2, 6, 7} answer L.H.S = R.H.S Hence proved