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 )

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

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 )

MEDIUM

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Determine whether the following statements are logically equivalent or not.

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

Important Questions on Mathematical Logic

EASY

Mathematics>Algebra>Mathematical Logic>Statements patterns and Logical Equivalence

T

denotes the contradiction then dual of the compounds statement

∽ p \land (q \lor c)

HARD

Mathematics>Algebra>Mathematical Logic>Statements patterns and Logical Equivalence

The negation of

∽ s \lor (∽ r \land s)

is equivalent to

EASY

Mathematics>Algebra>Mathematical Logic>Statements patterns and Logical Equivalence

Write the dual of

p \land ~ p \equiv F

EASY

Mathematics>Algebra>Mathematical Logic>Statements patterns and Logical Equivalence

Write the dual of the following statement;

"Shweta is a doctor or Seema is a teacher"

EASY

Mathematics>Algebra>Mathematical Logic>Statements patterns and Logical Equivalence

The dual of the statement pattern

~ p \land (q \lor t)

is (where

t

is a tautology and

c

is a contradiction)

HARD

Mathematics>Algebra>Mathematical Logic>Statements patterns and Logical Equivalence

The logical statement

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

is equivalent to

EASY

Mathematics>Algebra>Mathematical Logic>Statements patterns and Logical Equivalence

Write the dual of the following statement;

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

MEDIUM

Mathematics>Algebra>Mathematical Logic>Statements patterns and Logical Equivalence

The statement

(p \to q) \to [(~ p \to q) \to q]

MEDIUM

Mathematics>Algebra>Mathematical Logic>Statements patterns and Logical Equivalence

The Boolean expression

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

is equivalent to :

EASY

Mathematics>Algebra>Mathematical Logic>Statements patterns and Logical Equivalence

The compound statement

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

equivalent to:

EASY

Mathematics>Algebra>Mathematical Logic>Statements patterns and Logical Equivalence

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?

MEDIUM

Mathematics>Algebra>Mathematical Logic>Statements patterns and Logical Equivalence

The Boolean Expression

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

is equivalent to

HARD

Mathematics>Algebra>Mathematical Logic>Statements patterns and Logical Equivalence

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, ⊙)

MEDIUM

Mathematics>Algebra>Mathematical Logic>Statements patterns and Logical Equivalence

The statement pattern

(∽ p \land q)

is logically equivalent to

MEDIUM

Mathematics>Algebra>Mathematical Logic>Statements patterns and Logical Equivalence

The expression

~ (~ p \to q)

is logically equivalent to

MEDIUM

Mathematics>Algebra>Mathematical Logic>Statements patterns and Logical Equivalence

The contrapositive of the statement 'If two numbers are not equal, then their squares are not equal', is

MEDIUM

Mathematics>Algebra>Mathematical Logic>Statements patterns and Logical Equivalence

Which of the following statement pattern is a tautology?

MEDIUM

Mathematics>Algebra>Mathematical Logic>Statements patterns and Logical Equivalence

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>Statements patterns and Logical Equivalence

The negation of the Boolean expression

x \leftrightarrow ~ y

is equivalent to:

MEDIUM

Mathematics>Algebra>Mathematical Logic>Statements patterns and Logical Equivalence

The Boolean expression

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

is equivalent to

Determine whether the following statements are logically equivalent or not. ~(p∧q) and ~p∨~q

Important Questions on Mathematical Logic

Learn and Prepare for any exam you want !

Determine whether the following statements are logically equivalent or not.

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