Q 1: Find the identity element if a*b = a+b+ab , a, b € 1 Answer:

Q 2: Let a*b = l.c.m of (a,b), a, b € N, find 3*5 12 8 15

Q 3: Let * be a binary operation defined on Q. Check if a*b = ab, for a,b € Q is commutative. Yes No

Q 4: Let * be a binary operation defined on Q. Check if a*b = a^{2}+b^{2}, for a,b € Q is commutative. No Yes

Q 5: Let a * b be a binary operation on N given by a * b = l.c.m (a,b), a, b, € N, find 2*4 8 4 2

Q 6: Let * be a binary operation defined on Q. Find if a*b = ab/4 , for a,b € Q is associative. Answer:

Q 7: Let A = N x N and let * be a binary operation on A defined by (a,b)*(c,d) = (ac, bd). Show that (A,*) is associative. Answer:

Q 8: Let * be a binary operation defined on Q. Check if a*b = ab, for a,b € Q is associative. Answer:

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