JEE Main 2021 (Online) 31st August Morning Shift | Mathematical Reasoning Question 38 | Mathematics

JEE Main 2021 (Online) 31st August Morning Shift

MCQ (Single Correct Answer)

-1

Let *, ▢ $$\in$${$$\wedge$$, $$\vee$$} be such that the Boolean expression (p * $$\sim$$ q) $$\Rightarrow$$ (p ▢ q) is a tautology. Then :

* = $$\vee$$, ▢ = $$\vee$$

* = $$\wedge$$, ▢ = $$\wedge$$

* = $$\wedge$$, ▢ = $$\vee$$

* = $$\vee$$, ▢ = $$\wedge$$

JEE Main 2021 (Online) 27th August Evening Shift

MCQ (Single Correct Answer)

-1

The Boolean expression (p $$\wedge$$ q) $$\Rightarrow$$ ((r $$\wedge$$ q) $$\wedge$$ p) is equivalent to :

(p $$\wedge$$ q) $$\Rightarrow$$ (r $$\wedge$$ q)

(q $$\wedge$$ r) $$\Rightarrow$$ (p $$\wedge$$ q)

(p $$\wedge$$ q) $$\Rightarrow$$ (r $$\vee$$ q)

(p $$\wedge$$ r) $$\Rightarrow$$ (p $$\wedge$$ q)

JEE Main 2021 (Online) 27th August Morning Shift

MCQ (Single Correct Answer)

-1

The statement (p $$ \wedge $$ (p $$\to$$ q) $$\wedge$$ (q $$\to$$ r)) $$\to$$ r is :

a tautology

equivalent to p $$\to$$ $$\sim$$ r

a fallacy

equivalent to q $$\to$$ $$\sim$$ r

JEE Main 2021 (Online) 26th August Evening Shift

MCQ (Single Correct Answer)

-1

Consider the two statements :

(S1) : (p $$\to$$ q) $$ \vee $$ ($$ \sim $$ q $$\to$$ p) is a tautology .

(S2) : (p $$ \wedge $$ $$ \sim $$ q) $$ \wedge $$ ($$\sim$$ p $$\wedge$$ q) is a fallacy.

Then :

only (S1) is true.

both (S1) and (S2) are false.

both (S1) and (S2) are true.

only (S2) is true.

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