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Mathematical Reasoning

Short Answer Type

21. Are the following pairs of statements, negation of each other:

The number x is a rational number.
The number x is an irrational number.

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22. Are the following pairs of statements, negation of each other:

The number x is an odd number.

The number x is an even number.

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23.

Find the component statements of the following compound statements.

(i) It is raining and it is cold.

(ii) All the rational numbers are real and all the real numbers are complex.

(iii) 0 is a positive number or a negative number.

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Long Answer Type

24. Find the component statements of the following and check whether they are true or not.
(i) A square is a quadrilateral and its four sides equal.
(ii) All prime numbers are either even or odd.
(iii) A person who has taken Mathematics or Computer Science can go for MCA.
(iv) Chandigarh is the capital of Haryana and UP.
(v)

square root of 2

is a rational number or an irrational number.
(vi) 24 is a multiple of 2, 4 and 8.

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Short Answer Type

25. For the following compound statement, first identify the connecting word and then break it into component statement:
All rational numbers are real and all real numbers are not complex.

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26. For the following compound statement, first identify the connecting word and then break it into component statements:
Square of an integer is positive or negative.

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27. For the following compound statement, first identify the connecting word and then break it into component statements:
The sand heats up quickly in the Sun and does not cool down fast at night.

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28. For the following compound statement, first identify the connecting word and then break it into component statements:
x= 2 and x = 3 are the roots of the the equation 3x² - x - 10 = 0

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29. Write the component statements of the following compound statement and check whether the compound statement is true or false.
50 is a multiple of both 2 and 5.

The component statements are:
p : 50 is a multiple of 2
q : 50 is a multiple of 5
Here, both the component statements p and q are true.
Also, the connective is 'And'.
Hence, the compound statement is true.

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