Logic MCQs

Question 1

An axiom is a statement that is:

Accepted Answer

accepted as true without proof

Answer

shown false by an example

Answer

believed true but not yet proved

Answer

proved using other theorems

Question 2

Pythagoras' result a^2 + b^2 = c^2 for right triangles is:

Accepted Answer

a theorem

Answer

an axiom

Answer

a definition

Answer

a conjecture

Question 3

The expression n^2 + n + 41 is prime for n = 0, 1, 2, ldots, 39. For n = 40 its value is 1681 = 41^2. This shows that:

Accepted Answer

a pattern can fail even after many cases, so it needs a proof

Answer

40 cases make a proof

Answer

1681 is prime

Answer

the expression is always prime

Question 4

The sum of an even number 2m and an odd number 2n + 1 is:

Accepted Answer

2(m + n) + 1, which is odd

Answer

2(m + n), which is even

Answer

2mn + 1

Answer

m + n + 1

Question 5

A statement that has been proved is called a:

Accepted Answer

theorem

Answer

hypothesis

Answer

counterexample

Answer

conjecture

Question 6

In geometry, the word postulate means the same as:

Accepted Answer

axiom

Answer

conjecture

Answer

theorem

Answer

lemma

Question 7

A corollary is:

Accepted Answer

a result that follows directly from a theorem

Answer

a definition

Answer

an axiom

Answer

an unproved statement

Question 8

Which statement is an identity (true for every x)?

Accepted Answer

(x + 3)^2 = x^2 + 6x + 9

Answer

x + 3 = 7

Answer

(x + 3)^2 = x^2 + 3x + 9

Answer

(x + 3)^2 = x^2 + 9

Question 9

The sum of four consecutive integers n, n + 1, n + 2, n + 3 equals:

Accepted Answer

4n + 6 = 2(2n + 3)

Answer

4(n + 1)

Answer

4n + 4

Answer

4n + 10

Question 10

A conjecture is a statement that:

Accepted Answer

is believed to be true but has not been proved

Answer

is known to be false

Answer

has been proved

Answer

is accepted without proof

Question 11

The letters Q.E.D. at the end of a proof mean:

Accepted Answer

which was to be demonstrated (the proof is complete)

Answer

question ends directly

Answer

quite easily done

Answer

the next step follows

Question 12

A single example that shows a general statement is false is called a:

Accepted Answer

counterexample

Answer

proof

Answer

theorem

Answer

lemma

Question 13

“The angles of a triangle add up to 180^circ” is:

Accepted Answer

a theorem

Answer

a conjecture

Answer

an axiom

Answer

a definition

Question 14

Prove that the sum of three consecutive integers is divisible by 3. Writing them as n, n + 1, n + 2, the sum is:

Accepted Answer

3(n + 1)

Answer

3n + 2

Answer

3n

Answer

n + 3

Logic MCQs — Mathematics (page 3)

51. An axiom is a statement that is:

52. Pythagoras' result a^2 + b^2 = c^2 for right triangles is:

53. The expression n^2 + n + 41 is prime for n = 0, 1, 2, ldots, 39. For n = 40 its value is 1681 = 41^2. This shows that:

54. The sum of an even number 2m and an odd number 2n + 1 is:

55. A statement that has been proved is called a:

56. In geometry, the word postulate means the same as:

57. A corollary is:

58. Which statement is an identity (true for every x)?

59. The sum of four consecutive integers n, n + 1, n + 2, n + 3 equals:

60. A conjecture is a statement that:

61. The letters Q.E.D. at the end of a proof mean:

62. A single example that shows a general statement is false is called a:

63. “The angles of a triangle add up to 180^circ” is:

64. Prove that the sum of three consecutive integers is divisible by 3. Writing them as n, n + 1, n + 2, the sum is:

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