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Standard XI

Mathematics

Compound Statement

If p: Arjun i...

Question

If p: Arjun is the fastest q: Azad is the captain. Then which of the following denotes the compound statement: "Arjun is the fastest OR Azad is not the captain”

$p \land \sim q$

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$p \land q$

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$\sim p \lor \sim q$

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$p \lor \sim q$

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Solution

The correct option is D
$p \lor \sim q$

The connective used in the compound statement is OR which is denoted by the symbol ' $\lor$ ' and the second simple statement q is negated. Hence the denotation is given by $p \lor \sim q$ .

Try constructing the truth table too for $p \lor \sim q$ .

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Similar questions

Q. P: Arjun is the fastest. Q: Azad is the captain. denotes the statement "Arjun is the fastest OR Azad is not the captain"

Q. If p: Ridhi did not eat lunch q: Azad did not have lunch. Then which of the following denotes the compound statement: "Both Ridhi and Azad did not have lunch.”

Q. If the symbols have been assigned the meaning as given below:

P @ Q

\to

P is greater than Q

Q

\rightarrow$ P is either greater or equal to Q

P & Q

\to

P is smaller than Q

⋆

\to

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P = Q

\to

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Now assuming the given statements to be true, find which of the two conclusions I and II given below them is / are definitely true? Give answer.

Q. If the symbols have been assigned the meaning as given below:

P @ Q

\to

P is greater than Q

Q

\rightarrow$ P is either greater or equal to Q

P & Q

\to

P is smaller than Q

⋆

\to

P is either smaller than or equal to Q

P = Q

\to

P is equal to Q

Now assuming the given statements to be true, find which of the two conclusions I and II given below them is / are definitely true? Give answer.

Statements:

B @ V

K & C

⋆

Conclusions:

V @ C

B @ K

Q. If the symbols have been assigned the meaning as given below:

P @ Q

\to

P is greater than Q

Q

\rightarrow$ P is either greater or equal to Q

P & Q

\to

P is smaller than Q

⋆

\to

P is either smaller than or equal to Q

P = Q

\to

P is equal to Q

Now assuming the given statements to be true, find which of the two conclusions I and II given below them is / are definitely true? Give answer.

Statements:

L $ N

⋆

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If p: Arjun is the fastest q: Azad is the captain. Then which of the following denotes the compound statement: "Arjun is the fastest OR Azad is not the captain”

The correct option is D p∨∼q The connective used in the compound statement is OR which is denoted by the symbol '∨' and the second simple statement q is negated. Hence the denotation is given by p∨∼q. Try constructing the truth table too for p∨∼q.

The correct option is D
$p \lor \sim q$

The connective used in the compound statement is OR which is denoted by the symbol ' $\lor$ ' and the second simple statement q is negated. Hence the denotation is given by $p \lor \sim q$ .

Try constructing the truth table too for $p \lor \sim q$ .