To get the best deal on Tutoring, call 1-855-666-7440 (Toll Free)

Conjunction Worksheet

Conjunction Worksheet
  • Page 1
 1.  
Classify the disjunction as true, false or open: 0 < - 8 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.


Correct answer : (1)
 2.  
Establish the truth or falsity of the sentence '- (5 - 16) = 21 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.


Correct answer : (1)
 3.  
State whether the conjunction: All parallelograms are rectangles 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.


Correct answer : (2)
 4.  
Classify the disjunction: x + 5 ≥ 8 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.


Correct answer : (2)
 5.  
State whether the sentence 'Mercury is a star' or 'Uranus is a satellite' is true, false or open.
a.
"true#


Solution:

‘Mercury is a star’ is false.

‘Uranus is a satellite’ 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.


Correct answer : (-1)
 6.  
State whether the sentences 'He is the Mayor of our town' and '- 7 > - 9' is true, false or open.
a.
open
b.
true
c.
false


Solution:

’He is the Mayor of our Town’ is an open sentence.

- 7 > - 9 is true

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


Correct answer : (1)
 7.  
Classify the conjunction as true, false or open: 3 < 8 - 2 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.]


Correct answer : (2)
 8.  
Classify the conjunction: 2 + 3 = 5 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.

’As You Like It’ was written by Shakespeare is a true sentence.

Both sentences are true.

The conjunction is true.


Correct answer : (1)
 9.  
State whether the sentence is true, false or open: 4(2a + 7) = 8a + 28 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.


Correct answer : (3)
 10.  
State whether the sentence x < 11 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.


Correct answer : (3)

*AP and SAT are registered trademarks of the College Board.