Construct the truth table for the statements p ∨ q ∧ r .

Given, p ∨ q ∧ r We know that if p and q are two statements, then their conjunction ' p and q ' is represented by p ∧ q . The statement ' p ∧ q ' is true when both p and q are true, otherwise it is false. We know that if p and q are two statements, then their disjunction ' p or q ' is represented by p ∨ q . The statement ' p ∨ q ' is always true except when both p and q are false. Therefore, the truth table of the given statement is shown below: T denotes true and F denotes false. p q q p ∨ q p ∨ q ∧ r T T T T T T T F T F T F T T T F T T T T F T F T F F T T T T F F T F F F F F F F

Construct the truth table for the statements p ∧ q ∨ r .

Given, p ∧ q ∨ r We know that if p and q are two statements, then their conjunction ' p and q ' is represented by p ∧ q . The statement ' p ∧ q ' is true when both p and q are true, otherwise it is false. We know that if p and q are two statements, then their disjunction ' p or q ' is represented by p ∨ q . The statement ' p ∨ q ' is always true except when both p and q are false. Therefore, the truth table of the given statement is shown below: T denotes true and F denotes false. p q q p ∧ q p ∧ q ∨ r T T T T T T T F T T T F T F T F T T F T F T F F F F T T F T F F T F F F F F F F

Complete the truth table based on three input 'Or' gate. A B C D True False True True True True Where, D , is the output variable

Table II : A B C D True False True True True True True True

Table I : A B C D True False True False True True True True

Table III : A B C D True False True True True True True False

Form the conjunction of the statements p : 3 + 2 < 6 , q : 7 = 5 × 3 . What is its truth value?

Given, p : 3 + 2 < 6 q : 7 = 5 × 3 When two statements are joined by the connective 'and', the compound statement so formed is called the conjunction of the two statements. Therefore, p ∧ q : 3 + 1 < and 7 = 5 × 3 . The truth value of the statement p is T and q is F . We know that if p and q are two statements, then their conjunction ' p and q ' is represented by p ∧ q . The statement ' p ∧ q ' is true when both p and q are true, otherwise it is false. Therefore, p ∧ q i.e. the conjunction has the truth value F .

Direction: Select the correct statement corresponding to the symbols ~ p ∧ q . Statements: p: I play softball. q: The moon is 250 , 000 miles from Earth.

I don't play softball and the moon is 250 , 000 miles from Earth.

It is not the case that either I play softball or the moon is 250 , 000 miles from Earth.

I don't play softball or the moon is 250 , 000 miles from Earth.

It is not the case that both I play softball and the moon is 250 , 000 miles from Earth

EASY

Earn 100

Form the conjunction of the statements $p : - 2 - 3 = - 5$ , $q : - 5$ is a positive integer. What is its truth value?

Important Questions on Mathematical Logic

EASY

Mathematics>Algebra>Mathematical Logic>Logical Connectives and Negations

The negation of the statement ''

72

is divisible by

2

and

3

'' is

EASY

Mathematics>Algebra>Mathematical Logic>Logical Connectives and Negations

The negation of the statement "For all real numbers

x

and

y, x + y = y + x

" is

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Mathematics>Algebra>Mathematical Logic>Logical Connectives and Negations

The connective in the statement

2 + 7 > 9

2 + 7 < 9

EASY

Mathematics>Algebra>Mathematical Logic>Logical Connectives and Negations

The output of OR gate with two inputs A, B is low when _____.

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Mathematics>Algebra>Mathematical Logic>Logical Connectives and Negations

Form the disjunction of the statements

p : 3 = 4

q : 4

is a positive integer. What is its truth value?

EASY

Mathematics>Algebra>Mathematical Logic>Logical Connectives and Negations

Construct the truth table for the statements

(p \lor q) \land r

EASY

Mathematics>Algebra>Mathematical Logic>Logical Connectives and Negations

Which one of the structure is used to represent 'And' gate?

EASY

Mathematics>Algebra>Mathematical Logic>Logical Connectives and Negations

Check whether the following pair of statements are negation of each other. Give reasons for your answer.
$x + y = y + x$ is true for every real numbers $x$ and $y$ .
There exists real numbers $x$ and $y$ for which $x + y = y + x$ .