Verify (i) closure property (ii) commutative property (iii) associative property (iv) existence of identity and (v) existence of inverse for the operation `+_(5)` on `ZZ_5` using table corresponding to addition modulo 5.

Verify (i) closure property (ii) commutative property (iii) associative property (iv) existence of identity and (v) existence of inverse for the operation xx_(11) on a subset A = {1,3,4,5,9} of the set of remainders {0,1,2,3,4,5,6,7,8,9,10}.

Verify (i) closure property (ii) commutative property (iii) associate property (iv) existence of identity and (v) existence of inverse for the opertion xx 11 on a subset A = {1 , 3 , 4 , 5 , 9} of the set of the remainders { 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10}.

Verify (i) closure property (ii) commutative property and (iii) associati ve property of the following operation on the given set. (a•b) = a^(b) , forall a, b in NN (exponentiation property )

Let A be Q/{1}. Define * on A by x * y=x+y-xy. Is * binary on A? If so, examine the existence of identity & inverse properties for the operation * on A.

(i) Let M={({:(x,x),(x,x):}):x in R -{0}} and let ** be the matrix multiplication. Determine whether M is closed under ** . If so, examinie the existence of identity, existence of inverse properties for the operation ** on M.

By using the properties of definite integrals, evaluate the integrals int_(-5)^(5)abs(x+2)dx