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 the sets A and B denote the domain and range respectively of the function \(f(x)=\frac{1}{\sqrt[x]-x}\) where [x] denotes the smallest integer greater than or equal to x . Then among the statements
(S1) : A ∩ B = (1, ∞) – N and
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Questions Asked in JEE Main exam
Considering Bohr’s atomic model for hydrogen atom :
(A) the energy of H atom in ground state is same as energy of He+ ion in its first excited state.
(B) the energy of H atom in ground state is same as that for Li++ ion in its second excited state.
(C) the energy of H atom in its ground state is same as that of He+ ion for its ground state.
(D) the energy of He+ ion in its first excited state is same as that for Li++ ion in its ground state.- JEE Main - 2025
- Atomic Models
- In an adiabatic process, which of the following statements is true?
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- To obtain the given truth table, the following logic gate should be placed at G
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- Logic gates
- Choose the correct logic circuit for the given truth table having inputs A and B.
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A slanted object AB is placed on one side of convex lens as shown in the diagram. The image is formed on the opposite side. Angle made by the image with principal axis is:
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 "|".