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∨.
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∨.
Solution and Explanation
The binary operation ∨ on the set {1, 2, 3, 4, 5} is defined as a ∨ b = min {a, b} ∀ a, b ∈ {1, 2, 3, 4, 5}. Thus, the operation table for the given operation ∨ can be given as:
| ∨ | 1 | 2 | 3 | 4 | 5 |
| 1 | 1 | 1 | 1 | 1 | 1 |
| 2 | 1 | 2 | 2 | 2 | 2 |
| 3 | 1 | 2 | 3 | 3 | 3 |
| 4 | 1 | 2 | 3 | 4 | 4 |
| 5 | 1 | 2 | 3 | 4 | 5 |
Top Questions on Relations and Functions
- A relation $R$ on set $A=\{1,2,3\}$ defined as $R=\{(1,2),(2,1),(2,2)\}$ is
- CBSE CLASS XII - 2026
- Mathematics
- Relations and Functions
- Consider two sets \[ A = \{ x \in \mathbb{Z} : |(|x-3|-3)| \le 1 \} \] and \[ B = \left\{ x \in \mathbb{R} - \{1,2\} : \frac{(x-2)(x-4)}{x-1}\,\log_e(|x-2|) = 0 \right\}. \] Then the number of onto functions \( f : A \to B \) is equal to
- JEE Main - 2026
- Mathematics
- Relations and Functions
Let \( A = \{0,1,2,\ldots,9\} \). Let \( R \) be a relation on \( A \) defined by \((x,y) \in R\) if and only if \( |x - y| \) is a multiple of \(3\). Given below are two statements:
Statement I: \( n(R) = 36 \).
Statement II: \( R \) is an equivalence relation.
In the light of the above statements, choose the correct answer from the options given below.- JEE Main - 2026
- Mathematics
- Relations and Functions
- The number of relations, defined on the set \{a, b, c, d\}, which are both reflexive and symmetric, is equal to:
- JEE Main - 2026
- Mathematics
- Relations and Functions
- Show that the relation \( R \) in the set of natural numbers \( N \times N \) defined by \( (a, b)\, R\, (c, d) \) if \( a + d = b + c \) is an equivalence relation.
- Assam Board Class 12 - 2026
- Mathematics
- Relations and Functions
Questions Asked in CBSE CLASS XII exam
- A square loop of side 0.50 m is placed in a uniform magnetic field of 0.4 T perpendicular to the plane of the loop. The loop is rotated through an angle of 60° in 0.2 s. The value of emf induced in the loop will be:
- CBSE CLASS XII - 2026
- Electromagnetic induction
A racing track is built around an elliptical ground whose equation is given by \[ 9x^2 + 16y^2 = 144 \] The width of the track is \(3\) m as shown. Based on the given information answer the following:
(i) Express \(y\) as a function of \(x\) from the given equation of ellipse.
(ii) Integrate the function obtained in (i) with respect to \(x\).
(iii)(a) Find the area of the region enclosed within the elliptical ground excluding the track using integration.
OR
(iii)(b) Write the coordinates of the points \(P\) and \(Q\) where the outer edge of the track cuts \(x\)-axis and \(y\)-axis in first quadrant and find the area of triangle formed by points \(P,O,Q\).
- CBSE CLASS XII - 2026
- Integration
- Consider a cylindrical conductor of length \( l \) and area of cross-section \( A \). Current \( I \) is maintained in the conductor and electrons drift with velocity \( \vec{v}_d \, (|\vec{v}_d| = \frac{eE}{m} \tau) \), where symbols have their usual meanings. Show that the conductivity of the material of the conductor is given by \[ \sigma = \frac{n e^2 \tau}{m}. \]
- CBSE CLASS XII - 2026
- Current Density
- The painting Hazrat Nizamuddin Auliya and Amir Khusro belongs to which sub-school of Deccan Miniature?
- CBSE CLASS XII - 2026
- Indian Miniature Paintings and Museums
- (a) HACCP ensures food safety by identifying hazards. Give its full form.
(b) Describe four levels of food standards.- CBSE CLASS XII - 2026
- Fabric and Apparel
Concepts Used:
Binary Operation
A binary operation can be understood as a function f (x, y) that applies to two elements of the same set S, such that the result will also be an element of the set S. Examples of binary operations are the addition of integers, multiplication of whole numbers, etc. A binary operation is a rule that is applied on two elements of a set and the resultant element also belongs to the same set.
Properties of Binary Operation:
- Closure Property: A binary operation * on a non-empty set P has closure property, if a ∈ P, b ∈ P ⇒ a * b ∈ P.
- Associative Property: The associative property of binary operations holds if, for a non-empty set S, we can write (a * b) *c = a*(b * c), where {a, b, c} ∈ S. Commutative Property: A binary operation * on a non-empty set S is commutative, if a * b = b * a, for all (a, b) ∈ S. Suppose addition be the binary operation and N be the set of natural numbers.
- Distributive Property: Let * and # be two binary operations defined on a non-empty set S. The binary operations are distributive if, a* (b # c) = (a * b) # (a * c), for all {a, b, c} ∈ S. Suppose * is the multiplication operation and # is the subtraction operation defined on Z (set of integers).
- Identity Element: A non-empty set P with a binary operation * is said to have an identity e ∈ P, if e*a = a*e= a, ∀ a ∈ P. Here, e is the identity element.
- Inverse Property: A non-empty set P with a binary operation * is said to have an inverse element, if a * b = b * a = e, ∀ {a, b, e}∈P. Here, a is the inverse of b, b is the inverse of a and e is the identity element.
Read More: Truth Table
Types of Binary Operation:
There are four main types of binary operations which are: