Write the dual of p ∧ ~ p ≡ F .

To find the dual of p ∧ ~ p ≡ F In dual ∧ → ∨ , ∨ → ∧ , F → T , T → F Now let us make a truth table: p ~ p p ∧ ~ p T F F F T F Now, let us make truth table of p ∨ ~ p : p ~ p p ∨ ~ p T F T F T T Which gives p ∨ ~ p ≡ T Therefore, the dual of p ∧ ~ p ≡ F is p ∨ ~ p ≡ T

Write the dual of the following statement; ~ p ∧ ( q ∨ c ) .

The statement is ~ p ∧ ( q ∨ c ) Here, ∨ is the sign of disjunction, ∧ is the sign of conjunction and c is contradiction. To find the dual of the given statement, replace the conjunction sign ∧ with disjunction ∨ and disjunction sign ∨ with conjunction sign ∧ . And if there is any negation in the statement, do not change the negation of the statement. The duality of contradiction is tautology. So on replacing the connectives with each other, we get: ~ p ∨ ( q ∧ c )

The negation of the Boolean expression x ↔ ~ y is equivalent to:

( x ∧ y ) ∨ ( ~ x ∧ ~ y )

( ~ x ∧ y ) ∨ ( ~ x ∧ ~ y )

( x ∧ ~ y ) ∨ ( ~ x ∧ y )

( x ∧ y ) ∧ ( ~ x ∨ ~ y )

Let p , q , r be three logical statements. Consider the compound statements S 1 : ~ p ∨ q ∨ ~ p ∨ r and S 2 : p → q ∨ r Then, which of the following is NOT true?

If S 2 is False, then S 1 is True

If S 2 is True, then S 1 is True

If S 2 is False, then S 1 is False

If S 1 is False, then S 2 is False

EASY

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What is a Contingent Statement?

Important Questions on Mathematical Logic

EASY

Mathematics>Algebra>Mathematical Logic>Statement

Write the dual of

p \land ~ p \equiv F

MEDIUM

Mathematics>Algebra>Mathematical Logic>Statement

The Boolean expression

((p \land q) \lor (p \lor ~ q)) \land (~ p \land ~ q)

is equivalent to

EASY

Mathematics>Algebra>Mathematical Logic>Statement

Write the dual of the following statement;

$~ p \land (q \lor c)$ .

MEDIUM

Mathematics>Algebra>Mathematical Logic>Statement

The statement pattern

(∽ p \land q)

is logically equivalent to

MEDIUM

Mathematics>Algebra>Mathematical Logic>Statement

The negation of the Boolean expression

x \leftrightarrow ~ y

is equivalent to:

EASY

Mathematics>Algebra>Mathematical Logic>Statement

Write the dual of the following statement;

"Shweta is a doctor or Seema is a teacher"

MEDIUM

Mathematics>Algebra>Mathematical Logic>Statement

If the truth value of the Boolean expression $((p \lor q) \land (q \to r) \land (~ r)) \to (p \land q)$ is false, then the truth values of the statements $p, q, r$ respectively can be:

MEDIUM

Mathematics>Algebra>Mathematical Logic>Statement

p

and

q

are true and

r

and

s

are false statements, then which of the following is true?

EASY

Mathematics>Algebra>Mathematical Logic>Statement

The dual of the statement pattern

~ p \land (q \lor t)

is (where

t

is a tautology and

c

is a contradiction)

MEDIUM

Mathematics>Algebra>Mathematical Logic>Statement

The Boolean expression

(p \Rightarrow q) \land (q \Rightarrow ~ p)

is equivalent to :

EASY

Mathematics>Algebra>Mathematical Logic>Statement

Let $p, q, r$ be three logical statements. Consider the compound statements
$S_{1} : ((~ p) \lor q) \lor ((~ p) \lor r)$ and $S_{2} : p \to (q \lor r)$
Then, which of the following is NOT true?

HARD

Mathematics>Algebra>Mathematical Logic>Statement

The negation of

∽ s \lor (∽ r \land s)

is equivalent to

HARD

Mathematics>Algebra>Mathematical Logic>Statement

If the Boolean expression

(p \oplus q) \land (~ p ⊙ q)

is equivalent to

p \land q,

where

\oplus, ⊙ \in \{\land, \lor\},

then the ordered pair

(\oplus, ⊙)

EASY

Mathematics>Algebra>Mathematical Logic>Statement

c

denotes the contradiction then dual of the compounds statement

∽ p \land (q \lor c)

EASY

Mathematics>Algebra>Mathematical Logic>Statement

p \Rightarrow (q \lor r)

F a l s e

, then the truth values of

p, q, r

are respectively, (where

T

T r u e

and

F

F a l s e

)

MEDIUM

Mathematics>Algebra>Mathematical Logic>Statement

Which of the following is equivalent to the Boolean expression

p \land ~ q ?

EASY

Mathematics>Algebra>Mathematical Logic>Statement

Which of the following is not a logical statement?

EASY

Mathematics>Algebra>Mathematical Logic>Statement

The compound statement

(P \lor Q) \land (~ P) \Rightarrow Q

equivalent to:

MEDIUM

Mathematics>Algebra>Mathematical Logic>Statement

The Boolean Expression

(p \land \sim q) \lor q \lor (\sim p \land q)

is equivalent to

HARD

Mathematics>Algebra>Mathematical Logic>Statement

The logical statement

[~ (~ p \lor q) \lor (p \land r)] \land (~ q \land r)

is equivalent to

What is a Contingent Statement?

Important Questions on Mathematical Logic

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