Question:
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?"
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?"
Show Hint
Use logical operators systematically to convert English statements into symbolic form.
Updated On: Mar 26, 2025
- \( \neg (p \wedge q) \Rightarrow (r \wedge s) \)
- \( \neg (p \wedge \neg q) \Rightarrow (r \wedge s) \)
- \( \neg (p \wedge q) \Rightarrow (r \vee s) \)
- None of these
Hide Solution
Verified By Collegedunia
The Correct Option is A
Solution and Explanation
The given statement translates as:
{"If it does not rain or I do not go to school, then I shall meet my friend and go for a movie."}
The phrase "does not rain or do not go to school" can be written as:
\[
\neg (p \wedge q)
\]
The phrase "I shall meet my friend and go for a movie" translates to:
\[
r \wedge s
\]
Thus, the logical expression becomes:
\[
\neg (p \wedge q) \Rightarrow (r \wedge s)
\]
Was this answer helpful?
0
0
Top Questions on 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
- 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
- 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
- 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
The remainder on dividing $5^{99}$ by 11 is
- JEE Main - 2023
- Mathematics
- Statements
View More Questions
Questions Asked in BITSAT exam
- Let \( ABC \) be a triangle and \( \vec{a}, \vec{b}, \vec{c} \) be the position vectors of \( A, B, C \) respectively. Let \( D \) divide \( BC \) in the ratio \( 3:1 \) internally and \( E \) divide \( AD \) in the ratio \( 4:1 \) internally. Let \( BE \) meet \( AC \) in \( F \). If \( E \) divides \( BF \) in the ratio \( 3:2 \) internally then the position vector of \( F \) is:
- BITSAT - 2024
- Vectors
- Let \( \mathbf{a} = \hat{i} - \hat{k}, \mathbf{b} = x\hat{i} + \hat{j} + (1 - x)\hat{k}, \mathbf{c} = y\hat{i} + x\hat{j} + (1 + x - y)\hat{k} \). Then, \( [\mathbf{a} \, \mathbf{b} \, \mathbf{c}] \) depends on:}
- BITSAT - 2024
- Vectors
- Let the foot of perpendicular from a point \( P(1,2,-1) \) to the straight line \( L : \frac{x}{1} = \frac{y}{0} = \frac{z}{-1} \) be \( N \). Let a line be drawn from \( P \) parallel to the plane \( x + y + 2z = 0 \) which meets \( L \) at point \( Q \). If \( \alpha \) is the acute angle between the lines \( PN \) and \( PQ \), then \( \cos \alpha \) is equal to:
- The magnitude of projection of the line joining \( (3,4,5) \) and \( (4,6,3) \) on the line joining \( (-1,2,4) \) and \( (1,0,5) \) is:
- BITSAT - 2024
- Vectors
- The angle between the lines whose direction cosines are given by the equations \( 3l + m + 5n = 0 \) and \( 6m - 2n + 5l = 0 \) is:
- BITSAT - 2024
- Vectors
View More Questions