The contrapositive of the statement "if I am not feeling well, then I will go to the doctor" is :
- If I am feeling well, then I will not go to the doctor
- If I will go to the doctor, then I am feeling well
- If I will not go to the doctor, then I am feeling well
- If I will go to the doctor, then I am not feeling well.
The Correct Option is C
Solution and Explanation
Top Questions on Statements
- Let \( p, q, r \) be three logical statements. Consider the compound statements: \[ S_1: (\neg p \vee q) \vee (\neg p \vee r) \] \[ S_2: p \rightarrow (q \vee r) \] Which of the following is NOT true?
- BITSAT - 2024
- Mathematics
- Statements
- Consider the following statements:
\( A \): Rishi is a judge.
\( B \): Rishi is honest.
\( C \): Rishi is not arrogant.
The negation of the statement "If Rishi is a judge and he is not arrogant, then he is honest" is:- BITSAT - 2024
- Mathematics
- Statements
If
\( p \): It is raining today,
\( q \): I go to school,
\( r \): I shall meet my friends,
and \( s \): I shall go for a movie, then which of the following represents:
"If it does not rain or if I do not go to school, then I shall meet my friend and go for a movie?"- BITSAT - 2024
- Mathematics
- Statements
- Consider the following two propositions: $$ P_1: \neg (p \rightarrow \neg q) $$ $$ P_2: (p \wedge \neg q) \wedge ((\neg p) \vee q) $$ If the proposition $p \rightarrow ((\neg p) \vee q)$ is evaluated as FALSE, then:
- BITSAT - 2024
- Mathematics
- Statements
- If \( x \neq 0 \), then \[ \frac{\sin(\pi + x)\cos\left(\frac{\pi}{2} + x\right)\tan\left(\frac{3\pi}{2} - x\right)\cot(2\pi - x)}{\sin(2\pi - x)\cos(2\pi + x)\csc(-x)\sin\left(\frac{3\pi}{2} + x\right)} = \]
- MHT CET - 2024
- Mathematics
- Statements
Questions Asked in JEE Main exam
- The kinetic energy of translation of the molecules in 50 g of CO\(_2\) gas at 17°C is:
- JEE Main - 2025
- The Kinetic Theory of Gases
- Using the principal values of the inverse trigonometric functions the sum of the maximum and the minimum values of \(16((sec^{-1}x)^{2}+(cosec^{-1}x)^{2})\) is:
- JEE Main - 2025
- Inverse Trigonometric Functions
Consider the following sequence of reactions :
Molar mass of the product formed (A) is ______ g mol\(^{-1}\).- JEE Main - 2025
- Organic Chemistry
- A wire of resistance R is bent into an equilateral triangle and an identical wire is bent into a square. The ratio of resistance between the two end points of an edge of the triangle to that of the square is:
- JEE Main - 2025
- electrostatic potential and capacitance
In a Young's double slit experiment, three polarizers are kept as shown in the figure. The transmission axes of \( P_1 \) and \( P_2 \) are orthogonal to each other. The polarizer \( P_3 \) covers both the slits with its transmission axis at \( 45^\circ \) to those of \( P_1 \) and \( P_2 \). An unpolarized light of wavelength \( \lambda \) and intensity \( I_0 \) is incident on \( P_1 \) and \( P_2 \). The intensity at a point after \( P_3 \), where the path difference between the light waves from \( S_1 \) and \( S_2 \) is \( \frac{\lambda}{3} \), is:
- JEE Main - 2025
- electrostatic potential and capacitance
Concepts Used:
Statements
A statement is a sentence that is either true or false, but not both true and false simultaneously.
Types of Statements:
Simple Statement
- If a statement cannot be further broken down into various statements, or in simpler words if it is concrete by itself, it is called a Simple Statement.
- Examples include:
- A kite is not a rhombus.
- 15 is an odd number.
Compound Statement
- If a statement can further be broken down into simpler statements so that from a main statement, we can yield more than one statement, then it is called a Compound Statement.
- Consider the statement “10 is non-negative and a multiple of 5” which can be broken down into the statements: “10 is non-negative” and “10 is a multiple of 5”.
If-Then Statements
- If we encounter an if-then statement i.e. ‘if a then b’, then by proving that a is true, b can be proved to be true or if we prove that b is false, then a is also false.
- If we encounter a statement which says ‘a if and only if b’, then we can give reason for such a statement by showing that if a is true, then b is also true and if b is true, then a is also true.
- Example:
- a: 8 is multiple of 64
- b: 8 is a factor of 64
Since one of the given statements i.e. a is true, therefore, a or b is true.