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Question
Assertion :Let aN={aX:x∈N} then
3N∩7N={21,42,63,84...}. Reason: aN∩bN={λn:∈N,λ=L.C.M of (a,b)}.
Assertion :Let aN={aX:x∈N} then
3N∩7N={21,42,63,84...}. Reason: aN∩bN={λn:∈N,λ=L.C.M of (a,b)}.
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Solution
The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
aN={an:n∈N}={a,2a,3a,4a,...}
∴3N={3,6,9,12,15,18,21,24,27,30,...} and 7N={7,14,21,28,35,42,...}
∴3N∩7N={21,42,63,84,...}={1×21,2×21,3×21,4×21,...}={21n:n∈N}
={λ n,n∈N,λ=LCM of (3,7)}
aN={an:n∈N}={a,2a,3a,4a,...}
∴3N={3,6,9,12,15,18,21,24,27,30,...} and 7N={7,14,21,28,35,42,...}
∴3N∩7N={21,42,63,84,...}={1×21,2×21,3×21,4×21,...}={21n:n∈N}
={λ n,n∈N,λ=LCM of (3,7)}
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