# CBSE Class 11th Math 14 – Mathematical Reasoning MCQs

#### 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.

#### Converse of a conditional is equivalent to its ____.

Converse of a conditional is equivalent to its inverse.

#### 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 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 '↔'.

#### p: 3 is prime then ∼p is ____.

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

#### 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.

#### 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.

#### 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

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

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

#### 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.

#### 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.

#### "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.

#### 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

#### 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

#### 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.

#### Symbol for existential quantifier is ____.

Symbol for existential quantifier is ∃.

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

The 'or' used in the statement is exclusive.

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

p ⇒ q is an implication

#### 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.

#### 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.

#### 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.

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

Universal quantifier can be denoted by ∀.

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

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

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