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Mathematical Reasoning

Short Answer Type

31. Write the component statements of the following compound statement and check whether the compound statement is true or false.
Mumbai is the capital of Gujarat or Maharashtra.

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32. Write the component statements of the following compound statement and check whether the compound statement is true or false.
A rectangle is a quadrilateral or a 5-sided polygon.

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33.

State whether the “Or” used in the following statement is “exclusive “or” inclusive. Give reasons for your answer.
Sun rises or Moon sets.

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34.

State whether the “Or” used in the following statement is “exclusive “or” inclusive. Give reasons for your answer.
To apply for a driving licence, you should have a ration card or a passport.

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35.

State whether the “Or” used in the following statement is “exclusive “or” inclusive. Give reasons for your answer.
All integers are positive or negative.

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36.

Identify the type of “Or” used in the following statements and check whether the statements are true or false.

p : A square is a rectangle or a 7-sided polygon.
q : A square is a rectangle.
r : A square is a 7-sided polygon.

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37. Identify the quantifier in the following statement and write the negation of the statement.
For every real number x, x is less than x + 1.

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38. Identify the quantifier in the following statement and write the negation of the statement.
There exists a capital for every state in India.

Given statement is
p : There exists a capital for every state in India.
Here, the quantifier is "There exist".
The negation of given statement is
~p : It is not the case that there exists a capital for every state in India. Or
~p : There exists a state in india which does not have a captial.

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Long Answer Type

39. Write the component statements of the following compound statements and check whether the compound statement is true or false.

(i) A line is straight and extends indefinitely in both directions.
(ii) 0 is less than every positive integer and every negative integer.
(iii) All living things have two legs and two eyes.
(iv) A point occupies a position and its location can be determined.
(v) 42 is divisible by 5, 6 and 7.

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Short Answer Type

40. For the following statement, determine whether an “Or” inclusive or exclusive is used. Give reason for your answer.
An ice cream or pepsi is available with a Thali in a restaurant.

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