Binary Operation

Q.

Given relation $R=\left\{\right(1,2),(2,3\left)\right\}$ on the set $A=\{1,2,3\},$ the minimum number of ordered pairs which when added to

$R$ make it an equivalence relation is

1. $5$

2. $6$

3. $7$

4. $8$

Q.

How do you know if a determinant is zero?

Q.

Who is the father of number system?

Q.

Can you add determinants?

Q.

The number of binary operations that can be defined on the set $A=\left\{a,b,c\right\}$ is

1. $3^3$

2. $3^4$

3. $3^9$

4. $9^3$

Q.

Number of binary operations on the set {a, b} are

(A) 10 (B) 16 (C) 20 (D) 8

Q.

How much $-6$ is less than$-2$?

Q.

Write the remainder obtained when 1! + 2! + 3!+....+200! is divided by 14.

Q.

In $Z,$ the set of all integers, the inverse of $-7w.r.t.*$defined by $a*b=a+b+7,\forall a,b\in Z$ is

1. $-14$

2. $7$

3. $14$

4. $-7$

Q. Determine whether or not each of the definition of given below gives a binary operation. In the event that * is not a binary operation, give justification for this. (i) On Z + , define * by a * b = a − b (ii) On Z + , define * by a * b = ab (iii) On R , define * by a * b = ab 2 (iv) On Z + , define * by a * b = | a − b | (v) On Z + , define * by a * b = a

Q.

The basic operation performed by a computer are

Q. The least remainder when ${17}^{30}$ is divided by 5 is

1. 1
2. 2
3. 4
4. 3

Q.

Let * be an operation on Z be defined on Z as a* b = a^b for all a, b ϵ Z. Then which one of these options is correct?

1. a* b is an associative binary operation

2. a* b is a commutative binary operation

3. a* b is not a binary operation

4. a* b is a distributive binary operation

Q.

What is a closure property?

Q. Find the remainder when ${1021}^{1022}$ is divided by $1023.$
(correct answer + 2, wrong answer 0)

Q. Number of binary operations on the set { a , b } are (A) 10 (B) 16 (C) 20 (D) 8

Q. Let $\ast$ is a binary operation defined on $R$, if $a\ast b=a+b+6ab,$ then the value of $3\ast 2$ is ______

Q. State whether the following statements are true or false. Justify. (i) For an arbitrary binary operation * on a set N , a * a = a a * N . (ii) If * is a commutative binary operation on N , then a * ( b * c ) = ( c * b ) * a

Q.

Negation of “Ram is in Class $\text{X}$ or Rashmi is in Class $\text{XII}$” is

1. Ram is not in class $\text{X}$ but Ram is in class $\text{XII}$

2. Ram is not in class $\text{X}$ but Rashmi is not in class $\text{XII}$

3. Either Ram is not in Class $\text{X}$ or Ram is not in class $\text{XII}$

4. None of these

Q. Let $S$ be a set containing $n$ elements. Then the total number of binary operations on $S$ is

1. ${2^n}^2$
2. $n^2$
3. $n^n$
4. $n^{n^2}$

Q.

Find the identity element with respect to addition in integers?

1. $1$

2. $-1$

3. $0$

4. None

Q.

Fill In The Blanks ALU Is _____.

Q. Is * defined on the set {1, 2, 3, 4, 5} by a * b = L.C.M. of a and b a binary operation? Justify your answer.

Q. Consider the binary operation ∨ on the set {1, 2, 3, 4, 5} defined by a ∨ b = min { a , b }. Write the operation table of the operation∨.

Q. Consider a binary operation * on the set {1, 2, 3, 4, 5} given by the following multiplication table. (i) Compute (2 * 3) * 4 and 2 * (3 * 4) (ii) Is * commutative? (iii) Compute (2 * 3) * (4 * 5). (Hint: use the following table) * 1 2 3 4 5 1 1 1 1 1 1 2 1 2 1 2 1 3 1 1 3 1 1 4 1 2 1 4 1 5 1 1 1 1 5

Q. Let * ′ be the binary operation on the set {1, 2, 3, 4, 5} defined by a * ′ b = H.C.F. of a and b . Is the operation * ′ same as the operation * defined in Exercise 4 above? Justify your answer.

Q.

Convert hexadecimal to decimal directly.

Q.

Which of the following is not a binary operation defined on the set of positive real numbers?

1. Subtraction

2. Division

3. Multiplication

4. Addition

Q. If $a\ast b$ denotes the larger of ${}^{\prime }{a}^{\prime }$ and ${}^{\prime }{b}^{\prime }$ and if $aob$ = $(a\ast b)+3$, then write the value of $\left(5\right)o\left(10\right)$, where $\ast$ and $o$ are binary operations.

Q. Let * be the binary operation on N defined by a * b = H.C.F. of a and b . Is * commutative? Is * associative? Does there exist identity for this binary operation on N ?