Logic Worksheet

**Page 1**

1.

The basic axiom of algebra represented by (5 + 8) + 10 = 5 + (8 + 10) is ____

a. | associative property of addition | ||

b. | distributive property of addition | ||

c. | commutative property of addition | ||

d. | commutative property of multiplication |

It is in the form of (

So, the basic axiom of algebra represents the above is associative property of addition.

Correct answer : (1)

2.

The method of assuming the opposite of a statement is true. If this leads to impossibility, then the original statement is true is:

a. | A proof by contradiction | ||

b. | A Direct proof |

Correct answer : (1)

3.

The rule in mathematics that we accept to be true without proof is called:

a. | An axiom | ||

b. | A conjecture | ||

c. | A theorem |

Correct answer : (1)

4.

A statement that is believed to be true but not yet proved is:

a. | A theorem | ||

b. | An axiom | ||

c. | A conjecture |

Correct answer : (3)

5.

The basic axiom of algebra represented by 10 + (- 10) = 0 is

a. | Closure property of addition | ||

b. | Identity property of addition | ||

c. | Inverse property of addition | ||

d. | Inverse property of multiplication |

It is of the form

So, the basic axiom of algebra represents the above, is inverse property of addition.

Correct answer : (3)

6.

The basic axiom of algebra represented by 4 · ($\frac{1}{4}$) = 1, is

a. | Inverse property of multiplication | ||

b. | Distributive property of multiplication | ||

c. | Identity property of multiplication | ||

d. | Associative property of multiplication |

It is of the form

So, the basic axiom of algebra represents the above, is inverse property of multiplication.

Correct answer : (1)

7.

The statement: "There is no rational number whose square is 2", is:

a. | False | ||

b. | True |

So,

[Multiply each side by

This implies that 2 is a factor of

(2

[Replace

4

[Simplify.]

2

[Divide each side by 2.]

This implies that 2 is a factor of

So, 2 is a factor of both

This is impossible because

Therefore, it is impossible that there exists a rational number whose square is 2.

The statement: "There is no rational number whose square is 2", is true.

Correct answer : (2)

8.

The statement: "If $a$ and $b$ are both even integers, then their sum is even", is:

a. | True | ||

b. | False |

Then

[Assume the opposite of

[Subtract

[

This implies that

Therefore, it is impossible that

So,

Correct answer : (1)

9.

The basic axiom of algebra represented by $a$ × 1 = $a$ where $a$ is any real number, is:

a. | Associative property of multiplication | ||

b. | Inverse property of multiplication | ||

c. | Identity property of multiplication | ||

d. | Commutative property of multiplication |

The basic axiom of algebra represents the above, is identity property of multiplication.

Correct answer : (3)

10.

The basic axiom of algebra represented by 2$t$ + 7 = 7 + 2$t$, where $t$ is any real number, is

a. | Commutative property of addition | ||

b. | Associative property of addition | ||

c. | Inverse property of addition | ||

d. | Identity property of addition |

It is of the form

So, the basic axiom of algebra represents the above, is commutative property of addition.

Correct answer : (1)