Propositional Logic

Question 1

Define discrete mathematics

Answer 1

The part of mathematics devoted to the study of discrete (as opposed to continuous objects)

Question 2

Define propositions

Answer 2

Propositions is a declarative sentence that is either true or false

Question 3

Give an example of a proposition

Answer 3

“the moon is made out of cheese” (false)
1+0 = 1 (true)
0+0 = 2 (false)

Question 4

What are the atomic proposition variables

Answer 4

p, q, r, s …

Question 5

What are the atomic proposition constants

Answer 5

T(true), F (false)

Question 6

Show a negative proposition

Answer 6

¬p

Question 7

Show a conjunction

Answer 7

p ∧ q

Question 8

Show a disjunction

Answer 8

p ∨ q

Question 9

Show an implication

Answer 9

p → q

Question 10

Show a bioconditional

Answer 10

p ↔ q

Question 11

What does this symbol mean ∨

Answer 11

or

Question 12

What does this symbol mean ∧

Answer 12

and

Question 13

What does this symbol mean ↔

Answer 13

either not both / if and only i f

Question 14

What does this symbol mean –>

Answer 14

If, then

Question 15

When is a conjunction true

Answer 15

For a conjunction to be true both propositions must be true

Question 16

When is a disjunction true

Answer 16

For a disjunction to be true either proposition must be true

Question 17

How do you recognise a conjunction symbol

Answer 17

thing of construction as its similar to a roof of a house

Question 18

How do you recognise a disjunction symbol

Answer 18

a v symbol, think of Destruction

Question 19

When is a conjunction true

Answer 19

only when both propositions are true

Question 20

When is a disjunction true

Answer 20

it is true if it contains a true proposition

Question 21

When is an exclusive true

Answer 21

an exclusive is true when the propositions are different and not the same

Question 22

What does an implication do

Answer 22

creates a conditional statement

Question 23

What is the symbol for an implication

Answer 23

→ (an arrow pointing right)

Question 24

What does the proposition on the left of the arrow stand for

Answer 24

the hypothesis

Question 25

What does the proposition on the right of the arrow stand for

Answer 25

conclusion

Question 26

When does the proposition give a true result

Answer 26

both when the hypothesis is same as conclusion, but if hypothesis is false the p->q is always true

Question 27

State what is a tautology

Answer 27

A proposition that is always true

Question 28

State what is a contradiction

Answer 28

A proposition that is always false

Question 29

State what is a contingency

Answer 29

A proposition that is neither a tautology nor a contradiction