Advertisements
Advertisements
प्रश्न
Construct the composition table for +5 on set S = {0, 1, 2, 3, 4}.
Advertisements
उत्तर
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
संबंधित प्रश्न
Show that the binary operation * on A = R – { – 1} defined as a*b = a + b + ab for all a, b ∈ A is commutative and associative on A. Also find the identity element of * in A and prove that every element of A is invertible.
For each binary operation * defined below, determine whether * is commutative or associative.
On Z, define a * b = a − b
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.
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.
State whether the following statements are true or false. Justify.
For an arbitrary binary operation * on a set N, a * a = ∀ a a * N.
Given a non-empty set X, consider the binary operation *: P(X) × P(X) → P(X) given by A * B = A ∩ B &mnForE; A, B in P(X) is the power set of X. Show that X is the identity element for this operation and X is the only invertible element in P(X) with respect to the operation*.
Is * defined on the set {1, 2, 3, 4, 5} by a * b = LCM of a and b a binary operation? Justify your answer.
Let S = {a, b, c}. Find the total number of binary operations on S.
The binary operation * : R × R → R is defined as a * b = 2a + b. Find (2 * 3) * 4.
Let '*' be a binary operation on N defined by a * b = 1.c.m. (a, b) for all a, b ∈ N
Check the commutativity and associativity of '*' on N.
Determine which of the following binary operations are associative and which are commutative : * on Q defined by \[a * b = \frac{a + b}{2} \text{ for all a, b } \in Q\] ?
Check the commutativity and associativity of the following binary operations '*'. on Q defined by a * b = a − b for all a, b ∈ Q ?
Check the commutativity and associativity of the following binary operation '*' on N, defined by a * b = ab for all a, b ∈ N ?
Check the commutativity and associativity of the following binary operation '*' on N defined by a * b = gcd(a, b) for all a, b ∈ N ?
The binary operation * is defined by \[a * b = \frac{ab}{7}\] on the set Q of all rational numbers. Show that * is associative.
Define a binary operation on a set.
Define an associative binary operation on a set.
Write the total number of binary operations on a set consisting of two elements.
Write the inverse of 5 under multiplication modulo 11 on the set {1, 2, ... ,10}.
Write the composition table for the binary operation multiplication modulo 10 (×10) on the set S = {2, 4, 6, 8}.
A binary operation * is defined on the set R of all real numbers by the rule \[a * b = \sqrt{ a^2 + b^2} \text{for all a, b } \in R .\]
Write the identity element for * on R.
Mark the correct alternative in the following question:-
For the binary operation * on Z defined by a * b = a + b + 1, the identity element is ________________ .
Q+ denote the set of all positive rational numbers. If the binary operation a ⊙ on Q+ is defined as \[a \odot = \frac{ab}{2}\] ,then the inverse of 3 is __________ .
Let * be a binary operation on R defined by a * b = ab + 1. Then, * is _________________ .
On Z an operation * is defined by a * b = a2 + b2 for all a, b ∈ Z. The operation * on Z is _______________ .
Let * be a binary operation on Q+ defined by \[a * b = \frac{ab}{100} \text{ for all a, b } \in Q^+\] The inverse of 0.1 is _________________ .
Let * be an operation defined as *: R × R ⟶ R, a * b = 2a + b, a, b ∈ R. Check if * is a binary operation. If yes, find if it is associative too.
On Z, define * by (m * n) = mn + nm : ∀m, n ∈ Z Is * binary on Z?
Define an operation * on Q as follows: a * b = `(("a" + "b")/2)`; a, b ∈ Q. Examine the existence of identity and the existence of inverse for the operation * on Q.
Let A = `((1, 0, 1, 0),(0, 1, 0, 1),(1, 0, 0, 1))`, B = `((0, 1, 0, 1),(1, 0, 1, 0),(1, 0, 0, 1))`, C = `((1, 1, 0, 1),(0, 1, 1, 0),(1, 1, 1, 1))` be any three boolean matrices of the same type. Find A v B
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 = a2 + b2 ∀ 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
Let * be binary operation defined on R by a * b = 1 + ab, ∀ a, b ∈ R. Then the operation * is ______.
The binary operation * defined on set R, given by a * b `= "a+b"/2` for all a, b ∈ R is ____________.
The identity element for the binary operation * defined on Q – {0} as a * b = `"ab"/2 AA "a, b" in "Q" - {0}` is ____________.
Let * be a binary operation on the set of integers I, defined by a * b = a + b – 3, then find the value of 3 * 4.
Determine which of the following binary operation on the Set N are associate and commutaive both.
