Conjunction Worksheet

Conjunction Worksheet
• Page 1
1.
Classify the disjunction as true, false or open: 0 < - 8 $\mathrm{or}$ South Dakota is a state.
 a. true b. open c. none

Solution:

0 < - 8 is false

South Dakota is a state is true.

A disjunction is true if at least one of the sentences is true. So the disjunction is true.

2.
Establish the truth or falsity of the sentence '- (5 - 16) = 21 $\mathrm{or}$ 95 > - 95'.
 a. true b. open c. false

Solution:

- (5 - 16) = - (- 11) = 11
[Simplify.]

11 ≠ 21

So, - (5 - 16) = 21 is false.

95 > - 95 is true

One of the sentences is true, so the disjunction is true.

3.
State whether the conjunction: All parallelograms are rectangles $\mathrm{and}$ 2 - (- 3) < 5 + $z$ is true, false or open.
 a. true b. false

Solution:

All parallelograms are rectangles is a false sentence.

2 - (- 3) < 5 + z

5 < 5 + z

0 < z is open.
[Simplify.]

One of the sentences is false.

The conjunction is false.

4.
Classify the disjunction: $x$ + 5 ≥ 8 $\mathrm{or}$ - (- 19) ≥ 0 as true, false, or open.
 a. open b. true c. false

Solution:

x + 5 ≥ 8

or x ≥ 3 is an open sentence.

- (- 19) = 19 ≥ 0 is true.

One sentence is true, so the disjunction is true.

5.
State whether the sentence 'Mercury is a star' $\mathrm{or}$ 'Uranus is a satellite' is true, false or open.
 a. "true#

Solution:

Ã¢â‚¬ËœMercury is a starÃ¢â‚¬â„¢ is false.

Ã¢â‚¬ËœUranus is a satelliteÃ¢â‚¬â„¢ is false.

A disjunction is true only if at least one of the sentences is true.

Both sentences are false, so the disjunction is false.

6.
State whether the sentences 'He is the Mayor of our town' $\mathrm{and}$ '- 7 > - 9' is true, false or open.
 a. open b. true c. false

Solution:

Ã¢â‚¬â„¢He is the Mayor of our TownÃ¢â‚¬â„¢ is an open sentence.

- 7 > - 9 is true

The truth or falsity of the conjunction cannot be established, so it is an open sentence.

7.
Classify the conjunction as true, false or open: 3 < 8 - 2 $\mathrm{and}$ 8 > 64.
 a. true b. false c. open

Solution:

3 < 8 - 2

3 < 6 is true

8 > 64 is false

The conjunction is false.
[A conjunction can be true if and only if both the sentences are true.]

8.
Classify the conjunction: 2 + 3 = 5 $\mathrm{and}$ "As You Like It' was written by Shakespeare, as true, false or open.
 a. true b. false c. none

Solution:

2 + 3 = 5 is a true sentence.

Ã¢â‚¬â„¢As You Like ItÃ¢â‚¬â„¢ was written by Shakespeare is a true sentence.

Both sentences are true.

The conjunction is true.

9.
State whether the sentence is true, false or open: 4(2$a$ + 7) = 8$a$ + 28 $\mathrm{and}$ $x$ - 8 < 0.
 a. false b. true c. open

Solution:

4(2a + 7) = 4(2a) + 4(7)
[Distributive property.]

= 8a + 28

4(2a + 7) = 8a + 28 is true.

x - 8 < 0

x < 8 is open

The truth or falsity of the conjunction cannot be established, so it is an open sentence.

10.
State whether the sentence $x$ < 11 $\mathrm{or}$ $x$ ≥ 8 is true, false or open.
 a. false b. true c. open

Solution:

x < 11 is an open sentence.

x ≥ 8 is also an open sentence.

The truth or falsity of the disjunction cannot be established, the disjunction is open.