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Ex 3.3
Ex 3.3, 2
Ex 3.3, 3 You are here
Ex 3.3, 4 Important
Ex 3.3, 5 (i)
Ex 3.3, 5 (ii)
Ex 3.3, 6 (i)
Ex 3.3, 6 (ii) Important
Ex 3.3, 7 (i)
Ex 3.3, 7 (ii) Important
Ex 3.3, 8
Ex 3.3, 9
Ex 3.3, 10 (i) Important
Ex 3.3, 10 (ii)
Ex 3.3, 10 (iii) Important
Ex 3.3, 10 (iv)
Ex 3.3, 11 (MCQ) Important
Ex 3.3, 12 (MCQ)
Last updated at March 30, 2023 by Teachoo
Ex 3.3,3 If A’ = [■8(3&[email protected]−1&[email protected]&1)] and B =[■8(−1&2&[email protected]&2&3)] , then verify that (i) (A + B)’ = A’ + B’ Solving L.H.S (A + B)’ First finding A + B Given A’ = [■8(3&[email protected]−1&[email protected]&1)] A = (A’)’ = [■8(3&[email protected]−1&[email protected]&1)]^′ = [■8(3&−1&[email protected]&2&1)] Now, A + B = [■8(3&−1&[email protected]&2&1)] + [■8(−1&2&[email protected]&2&3)] = [■8(3+(−1)&−1+2&[email protected]+1&2+2&1+3)] = [■8(2&1&[email protected]&4&4)] So, (A + B)’ = [■8(2&[email protected]&[email protected]&4)] Solving R.H.S. (A’ + B’) Given A’ = [■8(3&[email protected]−1&[email protected]&1)] Also B = [■8(−1&2&[email protected]&2&3)] B’ = [■8(−1&[email protected]&[email protected]&3)] A’ + B’ = [■8(3&[email protected]−1&[email protected]&1)] + [■8(−1&[email protected]&[email protected]&3)] = [■8(3+(−1)&[email protected]−1+2&[email protected]+1&1+3)] = [■8(2&[email protected]&[email protected]&4)] = L.H.S Hence, L.H.S = R.H.S Hence proved Ex 3.3, 3 If A’ = [■8(3&[email protected]−1&[email protected]&1)] and B =[■8(−1&2&[email protected]&2&3)] , then verify that (ii) (A – B)’ = A’ – B’ Solving L.H.S (A – B)’ First finding A – B A – B = [■8(3&−1&[email protected]&2&1)] – [■8(−1&2&[email protected]&2&3)] = [■8(3−(−1)&−1−2&0−[email protected]−1&2−2&1−3)] = [■8(3+1&−3&−[email protected]&0&−2)] = [■8(4&−3&−[email protected]&0&−2)] (A – B)’ = [■8(4&[email protected]−3&[email protected]−1&−2)] Solving R.H.S A’ – B’ Given A’ = [■8(3&[email protected]−1&[email protected]&1)] B = [■8(−1&2&[email protected]&2&3)] B’ = [■8(−1&[email protected]&[email protected]&3)] A’ – B’ = [■8(3&[email protected]−1&[email protected]&1)] – [■8(−1&[email protected]&[email protected]&3)] = [■8(3−(−1)&4−[email protected]−1−2&2−[email protected]−1&1−3)] = [■8(3+1&[email protected]−3&[email protected]−1&−2)] = [■8(4&[email protected]−3&[email protected]−1&−2)] = L.H.S Hence, L.H.S = R.H.S Hence proved