Chapter 2 - Syntax and Symbolization

Question 1

What are logical connectives or operators?

Answer 1

They take atomic sentences and make compound sentences

Question 2

What are the logical connectives?

Answer 2

Conjunction
Disjunction
The Conditional
Negation

Question 3

List the logical connectives and their symbols:

Answer 3

Conjuction: and (&)
Disjunction: or (v)
The Conditional: if…then…(→)
Negation: not (¬)

Question 4

Either Bob has fed the ducks, or if he has fed the chickens, then the ducks are playing in the pond

Answer 4

(D V (C → P))

Question 5

If Bob is gathering eggs, then he has fed the chickens, or he has fed the ducks.

Answer 5

((B → C) V D)

Question 6

If he has fed the ducks, then Bob has not fed the chickens.

Answer 6

(D → ¬C)

Question 7

If Bob has fed the ducks and the chickens, then the ducks are playing in the pond.

Answer 7

((D & C) → P)

Question 8

Either Bob has fed the chickens if he has fed the ducks, or the ducks are playing in the pond.

Answer 8

((D → C) v. P)

Question 9

If Bob has not fed both the chickens and the ducks, then he is gathering eggs.

Answer 9

(~(C & D) -> B)

Question 10

((M & N)

Answer 10

It is an expression but it is not well-formed

Question 11

(J v. (K & L))

Answer 11

Not an expression. v. is not a basic symbol of sentential logic

Question 12

If the ducks are playing in the pond, then the chickens are playing in the pond only if Bob is chasing the fox away.

Answer 12

(P -> (S -> F))

Question 13

If the chickens are playing in the pond, then Bob both isn’t chasing the fox away and isn’t gathering eggs.

Answer 13

(S -> (~F & ~B))

Question 14

Put parentheses around the formula:

A & B v. C & D -> ~E & F

Answer 14

(((A & B) v. (C & D)) -> (~E & F))

Question 15

Put parentheses around the formula:

F -> D v. G -> ~D v. E

Answer 15

(((F -> D) v. G)) -> (~D v. E))