Mathematics Multiple Choice Questions on “Mathematical Reasoning – Special Words/Phrases”.
1. The compound statement with ‘And’ is true if ________ its component statements are __________
a) all, true
b) all, false
c) any, false
d) any, true
Answer: a
Clarification: The compound statement with ‘And’ can be true if all its component statements are true. If this condition is not satisfied, the compound statement cannot be true.
2. The compound statement with ‘And’ is false if ________ of its component statements are __________
a) all, true
b) all, false
c) any, false
d) any, true
Answer: c
Clarification: The compound statement with ‘And’ can be false if any of its component statements are false. All component statements can be false. In such case also, the compound statement will be false.
3. Which of the following compound statement is true?
a) 15 is divisible by 2 and 5
b) A prime number is even as well as odd
c) An elephant has two eyes and two ears
d) An even number is divisible by 2 and 4
Answer: c
Clarification: The compound statement with ‘And’ can be true if all its component statements are true. If this condition is not satisfied, the compound statement cannot be true.
15 is not divisible by 2 so it is false. A prime number cannot be even and odd at the same time so it is false. An even number is not always divisible by 4 so it is false. An elephant has two eyes as well as two ears so it is true.
4. Which of the following compound statement is true?
a) 1 is less than 2 and 3
b) 43 is prime as well as odd
c) 0 is positive and negative integer
d) 16 is divisible by 2 and 3
Answer: b
Clarification: The compound statement with ‘And’ can be true if all its component statements are true. If this condition is not satisfied, the compound statement cannot be true.
1 is neither less than 2 nor less than 3 so it is false. 43 is prime number as well as odd so it is true.
0 is neither positive number nor negative number. 16 is not divisible by 3 so it is false.
5. The compound statement with ‘Or’ is true if ________ its component statements are __________
a) all, true
b) all, false
c) any, false
d) any, true
Answer: d
Clarification: The compound statement with ‘Or’ can be true if any of its component statements are true. All component statements can be true. In such a case also, the compound statement will be true.
6. The compound statement with ‘Or’ is false if ________ of its component statements are __________
a) all, true
b) all, false
c) any, false
d) any, true
Answer: b
Clarification: The compound statement with ‘Or’ can be false if all its component statements are false. If this condition is not satisfied, the compound statement cannot be false.
7. If all the component statements can be true then the ‘Or’ is said to be ___________
a) Inclusive Or
b) Exclusive Or
c) Inclusive And
d) Exclusive And
Answer: a
Clarification: If all the component statements can be true simultaneously then ‘Or’ is said to be ‘Inclusive Or’.
8. If all the component statements cannot be true simultaneously then ‘Or’ is said to be __________
a) Inclusive Or
b) Exclusive Or
c) Inclusive And
d) Exclusive And
Answer: b
Clarification: If all the component statements can be true simultaneously then ‘Or’ is said to be ‘Exclusive Or’.
9. Students can take English or Hindi as fifth subject. Which phrase is used?
a) And
b) Exclusive Or
c) Inclusive Or
d) For all
Answer: b
Clarification: Students can take any one of English and Hindi as fifth subject so phrase used in the give statement is Exclusive Or.
10. People need Aadhar card or voter id to apply for Ration card. Which phrase is used?
a) And
b) Exclusive Or
c) Inclusive Or
d) For all
Answer: c
Clarification: Since people can have both Aadhar card and voter id. In such case also, they are eligible to apply for Ration card so phrase used is inclusive or.
11. Identify the type of Or and whether the statement “A square is a quadrilateral or pentagon” is true or not?
a) Inclusive Or, true
b) Exclusive Or, true
c) Inclusive Or, false
d) Exclusive Or, false
Answer: b
Clarification: Square is a quadrilateral is true so the statement is true. Square is not a pentagon so it is Exclusive Or.
12. Identify the type of Or and whether the statement “2 is a prime number or even number” is true or not?
a) Inclusive Or, true
b) Exclusive Or, true
c) Inclusive Or, false
d) Exclusive Or, false
Answer: a
Clarification: 2 is a prime number as well as even number. Since for the statement to be true, we need at least one to be true so it is true. Since both are correct so or used is Inclusive.
13. “All integers are positive or negative”. Is this ‘or’ is inclusive?
a) True
b) False
Answer: b
Clarification: We know, any integer cannot be positive as well as negative simultaneously so ‘or’ is exclusive. Hence it is false.
14. Which of the following is the negation of statement “a*b = b*a for every real number a and b”?
a) a*b ≠ b*a for every real number a and b
b) a*b = b*a for every real number a or b
c) There exists real number a and b for which a*b ≠ b*a
d) There exists real number a and b for which a*b = b*a
Answer: c
Clarification: Negation of for every is not for every. a*b = b*a not for every real number a and b.
This means There exists real number a and b for which a*b ≠ b*a.
15. Square of a natural number is positive or negative.
a) True
b) False
Answer: a
Clarification: We know, square of a natural is always positive. For a statement connected with ‘Or’, at least one of the component statements to be true so it is true.