The contrapositive of the statement "If you are born in India, then you are a citizen of India", is :
- If you are born in India, then you are not a citizen of India.
- If you are not a citizen of India, then you are not born in India.
- If you are a citizen of India, then you are born in India.
- If you are not born in India, then you are not a citizen of India.
The Correct Option is B
Solution and Explanation
Top Questions on 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
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- 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
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- 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
- 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
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Questions Asked in JEE Main exam
\( x \) is a peptide which is hydrolyzed to 2 amino acids \( y \) and \( z \). \( y \) when reacted with HNO\(_2\) gives lactic acid. \( z \) when heated gives a cyclic structure as below:
- JEE Main - 2025
- Elasticity
Statement-1: \( \text{ClF}_3 \) has 3 possible structures.
Statement-2: \( \text{III} \) is the most stable structure due to least lone pair-bond pair (lp-bp) repulsion.
Which of the following options is correct?
- JEE Main - 2025
- Molecular Stability
Consider the following graph between Rate Constant (K) and \( \frac{1}{T} \): Based on the graph, determine the correct order of activation energies \( E_{a1}, E_{a2}, \) and \( E_{a3} \).
- JEE Main - 2025
- Activation energy
- Maximum IE and minimum IE of group 13 elements are:
- JEE Main - 2025
- potential energy
- Statement-1: Alcohol is prepared from alkyl halide in the presence of aqueous KOH by elimination.
Statement-2: Alkenes are prepared from alkyl halide with alcoholic KOH by $\beta$-elimination.
Which of the following options is correct? 1. Statement-1 and Statement-2 are correct.
2. Statement-1 and Statement-2 are incorrect.
3. Statement-1 is true and Statement-2 is false.
4. Statement-1 is false and Statement-2 is true.
- JEE Main - 2025
- potential energy
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.