Which of the following statement is a tautology?
\((\sim q \land p) \land q\)
\((\sim q \land p) \land (p \land \sim p)\)
\((\sim q \land p) \lor (p \lor \sim p)\)
\((p \land q) \land (\sim (p \land q)\)
The Correct Option is C
Solution and Explanation
\(∵\) \((\sim q \land p) \lor (p \lor \sim p)\)
\(=\) \((\sim q \land p) \lor t\) (t is tautology) \(≡ t\)
So, the correct option is (C): \((\sim q \land p) \lor (p \lor \sim p)\)
Top Questions on Operations on Sets
- Let A,B,C are subsets of set X. Then consider the validity of the following set theoretic statement:
- WBJEE - 2023
- Mathematics
- Operations on Sets
- If A and B are disjoint sets and \(n(A)=4\) ,\(n(A∪B)=7\), then the value of \(n(B)\) is
- AP POLYCET - 2023
- Mathematics
- Operations on Sets
- If A= {P,O,L,Y,T,E,C,H,N, I} and B = {E, X, A, M}, then \(A∩B =\)
- TS POLYCET - 2023
- Mathematics
- Operations on Sets
- Let A be a set containing n elements, A subset P of A is chosen and set A is reconstructed by replacing the elements of P. A subset Q of A is chosen again. The number of ways of choosing P and Q such that Q contains just one element more than P is
- WBJEE - 2023
- Mathematics
- Operations on Sets
- If A = {1, 2, 3, 4, 5} and B={4, 5, 6, 7} then A-B=__
- TS POLYCET - 2023
- Mathematics
- Operations on Sets
Questions Asked in JEE Main exam
- The value of \( (\sin 70^\circ)(\cot 10^\circ \cot 70^\circ - 1) \) is:
- JEE Main - 2025
- Trigonometric Identities
- A force of 49 N acts tangentially at the highest point of a sphere (solid of mass 20 kg) kept on a rough horizontal plane. If the sphere rolls without slipping, then the acceleration of the center of the sphere is:
- JEE Main - 2025
- Quantum Mechanics
Let \( A = \{-3, -2, -1, 0, 1, 2, 3\} \). A relation \( R \) is defined such that \( xRy \) if \( y = \max(x, 1) \). The number of elements required to make it reflexive is \( l \), the number of elements required to make it symmetric is \( m \), and the number of elements in the relation \( R \) is \( n \). Then the value of \( l + m + n \) is equal to:
- JEE Main - 2025
- Sets and Relations
For hydrogen-like species, which of the following graphs provides the most appropriate representation of \( E \) vs \( Z \) plot for a constant \( n \)?
[E : Energy of the stationary state, Z : atomic number, n = principal quantum number]- JEE Main - 2025
- Hydrogen
- Concentrated nitric acid is labelled as 75%by mass. The volume in mL of the solution which contains 30 g of nitric acid is: Given: Density of nitric acid solution is 1.25 g/mL.
- JEE Main - 2025
- Solutions
Concepts Used:
Sets
Set is the collection of well defined objects. Sets are represented by capital letters, eg. A={}. Sets are composed of elements which could be numbers, letters, shapes, etc.
Example of set: Set of vowels A={a,e,i,o,u}
Representation of Sets
There are three basic notation or representation of sets are as follows:
Statement Form: The statement representation describes a statement to show what are the elements of a set.
- For example, Set A is the list of the first five odd numbers.
Roster Form: The form in which elements are listed in set. Elements in the set is seperatrd by comma and enclosed within the curly braces.
- For example represent the set of vowels in roster form.
A={a,e,i,o,u}
Set Builder Form:
- The set builder representation has a certain rule or a statement that specifically describes the common feature of all the elements of a set.
- The set builder form uses a vertical bar in its representation, with a text describing the character of the elements of the set.
- For example, A = { k | k is an even number, k ≤ 20}. The statement says, all the elements of set A are even numbers that are less than or equal to 20.
- Sometimes a ":" is used in the place of the "|".