Advertisements
Advertisements
Question
Construct the composition table for +5 on set S = {0, 1, 2, 3, 4}.
Solution
1 \[+_5\] 1 = Remainder obtained by dividing 1 + 1 by 5
= 2
3 \[+_5\] 4 = Remainder obtained by dividing 3 + 4 by 5
= 2
4 \[+_5\] 4 = Remainder obtained by dividing 4 + 4 by 5
= 3
So, the composition table is as follows :
| +5 | 0 | 1 | 2 | 3 | 4 |
| 0 | 0 | 1 | 2 | 3 | 4 |
| 1 | 1 | 2 | 3 | 4 | 5 |
| 2 | 2 | 3 | 4 | 0 | 1 |
| 3 | 3 | 4 | 0 | 1 | 2 |
| 4 | 4 | 0 | 1 | 2 | 3 |
APPEARS IN
RELATED QUESTIONS
For each binary operation * defined below, determine whether * is commutative or associative.
On Z+, define a * b = ab
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∨.
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.
Discuss the commutativity and associativity of binary operation '*' defined on A = Q − {1} by the rule a * b= a − b + ab for all, a, b ∊ A. Also find the identity element of * in A and hence find the invertible elements of A.
Determine whether or not the definition of * given below gives a binary operation. In the event that * is not a binary operation give justification of this.
On Z+, defined * by a * b = a − b
Here, Z+ denotes the set of all non-negative integers.
Determine whether or not the definition of *given below gives a binary operation. In the event that * is not a binary operation give justification of this.
On Z+, defined * by a * b = ab
Here, Z+ denotes the set of all non-negative integers.
Let * be a binary operation on the set I of integers, defined by a * b = 2a + b − 3. Find the value of 3 * 4.
Let S = {a, b, c}. Find the total number of binary operations on S.
Check the commutativity and associativity of the following binary operation '*' on Q defined by \[a * b = \frac{ab}{4}\] for all a, b ∈ Q ?
If the binary operation o is defined by aob = a + b − ab on the set Q − {−1} of all rational numbers other than 1, shown that o is commutative on Q − [1].
Find the identity element in the set of all rational numbers except −1 with respect to *defined by a * b = a + b + ab.
Let * be a binary operation on Z defined by
a * b = a + b − 4 for all a, b ∈ Z Find the identity element in Z ?
Let * be a binary operation on Q − {−1} defined by a * b = a + b + ab for all a, b ∈ Q − {−1} Show that every element of Q − {−1} is invertible. Also, find the inverse of an arbitrary element ?
Let R0 denote the set of all non-zero real numbers and let A = R0 × R0. If '*' is a binary operation on A defined by
(a, b) * (c, d) = (ac, bd) for all (a, b), (c, d) ∈ A
Show that '*' is both commutative and associative on A ?
Let R0 denote the set of all non-zero real numbers and let A = R0 × R0. If '*' is a binary operation on A defined by
(a, b) * (c, d) = (ac, bd) for all (a, b), (c, d) ∈ A
Find the invertible element in A ?
Let A \[=\] R \[\times\] R and \[*\] be a binary operation on A defined by \[(a, b) * (c, d) = (a + c, b + d) .\] . Show that \[*\] is commutative and associative. Find the binary element for \[*\] on A, if any.
Construct the composition table for ×4 on set S = {0, 1, 2, 3}.
For the binary operation ×10 on set S = {1, 3, 7, 9}, find the inverse of 3.
Find the inverse of 5 under multiplication modulo 11 on Z11.
Define a binary operation on a set.
Define an associative binary operation on a set.
For the binary operation multiplication modulo 5 (×5) defined on the set S = {1, 2, 3, 4}. Write the value of \[\left( 3 \times_5 4^{- 1} \right)^{- 1}.\]
Let +6 (addition modulo 6) be a binary operation on S = {0, 1, 2, 3, 4, 5}. Write the value of \[2 +_6 4^{- 1} +_6 3^{- 1} .\]
The law a + b = b + a is called _________________ .
Let * be a binary operation on N defined by a * b = a + b + 10 for all a, b ∈ N. The identity element for * in N is _____________ .
Let * be a binary operation defined on Q+ by the rule
\[a * b = \frac{ab}{3} \text{ for all a, b } \in Q^+\] The inverse of 4 * 6 is ___________ .
Let '*' be a binary operation on N defined by
a * b = 1.c.m. (a, b) for all a, b ∈ N
Find 2 * 4, 3 * 5, 1 * 6.
Determine whether * is a binary operation on the sets-given below.
(a * b) = `"a"sqrt("b")` is binary on R
Let M = `{{:((x, x),(x, x)) : x ∈ "R"- {0}:}}` and let * be the matrix multiplication. Determine whether M is closed under * . If so, examine the existence of identity, existence of inverse properties for the operation * on M
Choose the correct alternative:
If a * b = `sqrt("a"^2 + "b"^2)` on the real numbers then * is
Let * be the binary operation defined on Q. Find which of the following binary operations are commutative
a * b = a – b ∀ a, b ∈ Q
Let * be the binary operation defined on Q. Find which of the following binary operations are commutative
a * b = (a – b)2 ∀ a, b ∈ Q
The binary operation * defined on set R, given by a * b `= "a+b"/2` for all a, b ∈ R is ____________.
The binary operation * defined on N by a * b = a + b + ab for all a, b ∈ N is ____________.
If * is a binary operation on the set of integers I defined by a * b = 3a + 4b - 2, then find the value of 4 * 5.
Let * be the binary operation on N given by a * b = HCF (a, b) where, a, b ∈ N. Find the value of 22 * 4.
Which of the following is not a binary operation on the indicated set?
