EASY
Earn 100

let * be a binary operation on Rdefined by a*b=a4+b7,a,bR.Show that * is not commutative and associative.

Important Questions on Set Theory and Relations

MEDIUM
Let * be a binary operation on the set Q of rational numbers, then a*b=a-b2 is
EASY

Let A=N×N and '*' be a binary operation on A defined by (a,b)*(c,d)=(a+c,b+d).

Prove that '*' is associative.

EASY
Prove that the binary operation * defined by a*b=a+b+ab in the set N is associative.
EASY
On the set of positive rationals, a binary operation * is defined by a*b=2ab5. If 2*x=3-1 then x=
MEDIUM
State all the five properties of groups.
EASY
Let N denote the set of all natural numbers. Define two binary relations on N as R1=x,yN×N:2x+y=10 and R2=x,yN×N:x+2y=10. Then
EASY
Show that : R×RR defined by a * b=a+2 b is neither commutative nor associative.
MEDIUM
If n(A)=2 and total number of possible relations from set A to set B is 1024, then n(B) is
MEDIUM

Show that the set of all non-zero rational numbers is not closed under addition.

EASY
Let * be a binary operation on Q, defined by a*b=ab2;a,bQ. Determine whether *  is associative or not.
MEDIUM
For the binary operation * defined on R1 by the rule a*b=a+b+ab for all a, bR1, the inverse of a is
EASY
Examine whether the operation  defined on R by a a b=ab+1 is  a binary. is it associative or not ?
MEDIUM
If R=x, y:x, yZ, x2+3y28 is a relation on the set of integers Z, then the domain of R-1 is
EASY
The binary operation * on the set + of positive real numbers defined by a*b=ab is
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If A=a,b,c, then the number of binary operations on A is
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Consider the following relations in the real numbers R1=(x,y)x2+y225 and R2=(x,y),y4x29, then the range of R1R2 is
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Let* be a binary operation on the set R of real numbers defined by a*b=3ab7, then the identity element in R for * is
EASY

Let A=N×N and '*' be a binary operation on A defined by (a,b)*(c,d)=(a+c,b+d).

Prove that '*' is commutative

MEDIUM
Show that "*" on Q defined by a*b=ab+1 is commutative but not associative.
EASY
In a group G, the equations ax=b and ya=b have