#### If 'p' is a statement, the negation of the statement is denoted by ____.

If 'p' is a statement, the negation of the statement is denoted by ∼p.

#### The truth value of the conjunction is true, if the truth values of all the component statements are true.

The truth value of the conjunction is true, if the truth values of all the component statements are true.

#### Which of following is a statement.

Two plus three is five. This sentence is true. Hence, it is a statement. Have you seen Hyderabad? This sentence is neither true nor false. Hence, it is not a statement. He is very talented. This is only a sentence not a statement because we need further information to decide whether the sentence is true or false. Hence, it is not a statement. x^{2}+y^{2}= 100 is not a statement.

#### Truth value of p: 3 × 7 = 21 and q: 4 + 3 = 7 is true.

Truth value of p: 3 × 7 = 21 and q: 4 + 3 = 7 is true.

#### If p ⇒ q is an implication then its contrapositive is ____.

If p ⇒ q is an implication then its contrapositive is ~q ⇒ ~p.

#### If a given statement is true, its negation will be false. If a given statement is false its negation will be true.

If a given statement is true, its negation will be false. If a given statement is false its negation will be true.

#### p: Taj Mahal is in Agra q: Kutub Minar is in Delhi. The disjunction of the above statements is, Taj Mahal is in Agra or Kutub Minar is in Delhi.

Given, p: Taj Mahal is in Agra q: Kutub Minar is in Delhi P ∨ q: Taj Mahal is in Agra or Kutub Minar is in Delhi.

#### Which of following is not a statement.

Clse the door. This sentence is neither true nor false (It is a command). Hence, it is not a statement. Sun is a planet. This sentence is false (Sun is a star). Hence, it is a statement. Nikhil is a boy. This sentence is true. Hence, it is a statement. Newyork is in India. This sentence is false (Newyork is in USA) Hence, it is a statement

#### Which of the following is an implication.

p ⇒ q is an implication

#### Universal quantifier can be denoted by ____.

Universal quantifier can be denoted by ∀.

#### A compound statement formed by combining two or more statements by using the word "and" is ____.

A compound statement formed by combining two or more statements by using the word "and" is called their conjunction.

#### Form the disjunction of the following simple statements. p: Ram is playing q: Shyam is sleeping.

p: Ram is playing q: Shyam is sleeping Disjunction: Ram is playing or Shyam is sleeping

#### A statement is a sentence which is either true or false but not both.

A statement is a sentence which is either true or false but not both.

#### A compound statement formed by combining two or more statements by using the word "or" is called their disjunction.

A compound statement formed by combining two or more statements by using the word "or" is called their disjunction.

#### p: Sun is hot q: Earth is round. The conjunction of the above statements is, Sun is hot or earth is round.

Given, p: Sun is hot q: Earth is round p ∨ q: Sun is hot and earth is round.

#### "Four multiplied by three is ten" is a statement.

Four multiplied by three is ten. This sentence is false (∵ 4 × 3 = 12) Hence, it is a statement.

#### If two statements have the same truth values, such statements are called equivalent statements. To indicate that two statments are ‘equal’ we use the symbol ____.

If two statements have the same truth values, such statements are called equivalent statements. To indicate that two statments are 'equal' we use the symbol '↔'.

#### A bi-implication p ⇔ q is true, when:

A bi-implication p ⇔ q is true, when both p and q are true.

#### Translate the following statement into symbolic form. "Mona and Shyam went to Mumbai".

The symbolic form of the given statement will be p ∧ q, where p: Mona went to Mumbai. q: Shaym went to Mumbai.

#### p: 3 is prime then ∼p is ____.

p : 3 is prime then ∼p is 3 is not prime.

#### Symbol for existential quantifier is ____.

Symbol for existential quantifier is ∃.

#### An implication p ⇒ q is false, when:

An implication p ⇒ q is false, when p is true and q is false.

#### Let p be "She is beautiful" and q be "She is happy". Write each of the following statements that are in symbolic form into English sentences.

p ∧ q: She is beautiful and she is happy

#### 'Or' is used in the following statement is exclusive. Sun rises or Moon sets.

The 'or' used in the statement is exclusive.

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