If p : It raining today, q: I go to school, r : I shall meet any...

If p : It raining today,

\mathrm{q}:

I go to school, r : I shall meet any friends and s : I shall go for a movie, then which of the following is the proposition : 'If it does not rain or if I do not go to school, then I shall meet my friend and go for a movie'?

Options

A $\sim(p \wedge q) \Rightarrow(r \wedge s)$
B $\sim(\mathrm{p} \wedge \sim \mathrm{q}) \Rightarrow(\mathrm{r} \wedge \mathrm{s})$
C $\sim(p \wedge q) \Rightarrow(r \vee s)$
DNone of these

Correct answer

A. $\sim(p \wedge q) \Rightarrow(r \wedge s)$

Step-by-step solution

Correct result is

(\sim \mathrm{p} \vee \sim \mathrm{q}) \Rightarrow(\mathrm{r} \wedge \mathrm{s})

So,

\sim(p \wedge q) \Rightarrow(r \wedge s)

Practice Mathematical Reasoning on Quantrex Academy →

More from Mathematical Reasoning

The Boolean expression ∼(p ∨ q) ∨(∼ p ∧ q) is equivalent to BITSAT 2024 If p: 2 is an even number q: 2 is a prime number, r: 2+2=2^2 Then the symbolic statement… BITSAT 2024 Consider the following statements : A: Rishi is a judge. B : Rishi is honest. C: Rishi is… BITSAT 2024 Let p, q, r be three logical statements. Consider the compound statements S_1:((∼ p) ∨ q)… BITSAT 2024 Consider the following two propositions: P_1: ∼(p arrow ∼ q)P_2:(p ∧ ∼ q) ∧((∼ p) ∨ q) If… BITSAT 2024 The negation of the Boolean expression ((∼ q)∧ p) ⇒((∼ p) ∨ q) is logically equivalent to BITSAT 2023 Negation of the Boolean expression p ⇔(q ⇒ p) is BITSAT 2023 The statement p: For any real numbers x, y if x=y , then 2 x+a=2 y+a when a ∈ Z . BITSAT 2021 Which of the following statement is a tautology? BITSAT 2018 If p: 4 is an even prime number, q: 6 is a divisor of 12 and r: the HCF of 4 and 6 is 2… BITSAT 2018 Inthetruth table for the statement (p ∧ q) arrow(q ∨ ∼ p) , the last column has the truth… BITSAT 2013 Negation of "Paris in France and London is in England" is BITSAT 2011 If f(t)=(1-t)/(1+t) , then f^ (1 / t) is equal to BITSAT 2009 Full Mathematical Reasoning list Mathematical Reasoning JEE Maths PYQs JEE Mathematics PYQs All BITSAT PYQs