Description

I need someone to give me the answers to these questions please. This is for formal logic course.

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QUESTION 1

The following symbolic expression is well-formed according to the grammar of our formal language.

A7 B

True

False

QUESTION 2

The following symbolic expression is well-formed according to the grammar of our formal language

77 (P → (P → (P → P))) (Q 7. (Q (Q = Q)))

True

False

QUESTION 3

The following symbolic expression is well-formed according to the grammar of our formal language

A# (B → (C v D))

True

False

OUESTION A

QUESTION 14

You are given the key to translate from our formal language into English.

KEY:

R: It rains.

• C: the game is canceled.

• F: the ball floats in water.

S: the game is rescheduled.

R>G F→G C17 S))

a. If it rains, then if the ball does not float in water the game is neither canceled nor rescheduled.

b. Only if it rains and the ball floats in water is the game neither canceled nor rescheduled.

c. The game is neither canceled nor rescheduled if and only if it rains and the ball does not float in water.

d. The game is not canceled and not rescheduled but it rains and the ball floats in water.

QUESTION 1

The following symbolic expression is well-formed according to the grammar of our formal language.

A7 B

True

False

QUESTION 2

The following symbolic expression is well-formed according to the grammar of our formal language

77 (P → (P → (P → P))) (Q 7. (Q (Q = Q)))

True

False

QUESTION 3

The following symbolic expression is well-formed according to the grammar of our formal language

A# (B → (C v D))

True

False

OUESTION A

QUESTION 4

The following symbolic expression is well-formed according to the grammar of our formal language

PV QAR

True

False

QUESTION 5

The following symbolic expression is well-formed according to the grammar of our formal language

7

| A →7 (B A (B V A)

True

False

QUESTION 6

What is the main connective symbol of the formula given below?

7 ((A → B) ^ (A →7 B))

a. >

a

b. A

O

C.

7 – FIRST FROM THE LEFT

d

d. →

QUESTION 7

What is the main connective symbol of the formula given below?

(P →Q) →GQ 7 P)

a. >- first from the left

b. →

second from the left

C. 7

first from the left

d. →

– third from the left

QUESTION 8

What is the main connective symbol of the formula given below?

*, B) 4 (P → (Q v C))

(A

a. >

O b. 1

C. –

O d. V

QUESTION 14

You are given the key to translate from our formal language into English.

KEY:

R: It rains.

• C: the game is canceled.

• F: the ball floats in water.

S: the game is rescheduled.

R>G F→G C17 S))

a. If it rains, then if the ball does not float in water the game is neither canceled nor rescheduled.

b. Only if it rains and the ball floats in water is the game neither canceled nor rescheduled.

c. The game is neither canceled nor rescheduled if and only if it rains and the ball does not float in water.

d. The game is not canceled and not rescheduled but it rains and the ball floats in water.

QUESTION 11

You are given the key to translate from English into our formal language.

KEY:

R: It rains.

C: the game is canceled.

F: the ball floats in water.

S: the game is rescheduled.

If it rains but the ball does not float in water, then the game is not canceled.

a. (R

→7 F) →7 C

Ob.(RAF) →C

C. (R V7 F)

yo

O d.(R → F) →7 C

QUESTION 12

You are given the key to translate from English into our formal language.

KEY:

• R: It rains.

• C: the game is canceled.

F: the ball floats in water.

S: the game is rescheduled.

.

The game is canceled only if it both rains and the ball floats in water.

a. C«> (RAF)

O b. (RAF) => C

Oc. (RAF) →

C

Od. C>(RAF)

QUESTION 13

You are given the key to translate from our formal language into English.

KEY:

• R: It rains.

• C: the game is canceled.

• F: the ball floats in water.

• S: the game is rescheduled.

(CAS) => (R v F)

a. The game is canceled and rescheduled only if it rains or the ball floats in water.

b. The game is canceled and rescheduled if and only if it rains or the ball floats in water.

c. If the game is canceled and rescheduled, then either it rains or the ball floats in water.

d. If it rains or the ball floats in water, then the game is canceled and rescheduled.

QUESTION 14

QUESTION 9

Which connective is defined by the following truth table?

р

q

(p

9)

T

T

T

T

T

T

F

T

F.

F

F

T

F.

T

T

F

F

F

T

F

a.

(name of connective: conditional)

O b. =>

(name of connective: biconditional)

O c. V

(name of connective: inclusive disjunction)

1

O d.

(name of connective: conjunction)

QUESTION 14

You are given the key to translate from our formal language into English.

KEY:

R: It rains.

• C: the game is canceled.

• F: the ball floats in water.

S: the game is rescheduled.

R>G F→G C17 S))

a. If it rains, then if the ball does not float in water the game is neither canceled nor rescheduled.

b. Only if it rains and the ball floats in water is the game neither canceled nor rescheduled.

c. The game is neither canceled nor rescheduled if and only if it rains and the ball does not float in water.

d. The game is not canceled and not rescheduled but it rains and the ball floats in water.

QUESTION 14

You are given the key to translate from our formal language into English.

KEY:

R: It rains.

• C: the game is canceled.

• F: the ball floats in water.

S: the game is rescheduled.

R>G F→G C17 S))

a. If it rains, then if the ball does not float in water the game is neither canceled nor rescheduled.

b. Only if it rains and the ball floats in water is the game neither canceled nor rescheduled.

c. The game is neither canceled nor rescheduled if and only if it rains and the ball does not float in water.

d. The game is not canceled and not rescheduled but it rains and the ball floats in water.

QUESTION 9

Which connective is defined by the following truth table?

р

q

(p

9)

T

T

T

T

T

T

F

T

F.

F

F

T

F.

T

T

F

F

F

T

F

a.

(name of connective: conditional)

O b. =>

(name of connective: biconditional)

O c. V

(name of connective: inclusive disjunction)

1

O d.

(name of connective: conjunction)

QUESTION 11

You are given the key to translate from English into our formal language.

KEY:

R: It rains.

C: the game is canceled.

F: the ball floats in water.

S: the game is rescheduled.

If it rains but the ball does not float in water, then the game is not canceled.

a. (R

→7 F) →7 C

Ob.(RAF) →C

C. (R V7 F)

yo

O d.(R → F) →7 C

QUESTION 12

You are given the key to translate from English into our formal language.

KEY:

• R: It rains.

• C: the game is canceled.

F: the ball floats in water.

S: the game is rescheduled.

.

The game is canceled only if it both rains and the ball floats in water.

a. C«> (RAF)

O b. (RAF) => C

Oc. (RAF) →

C

Od. C>(RAF)

QUESTION 13

You are given the key to translate from our formal language into English.

KEY:

• R: It rains.

• C: the game is canceled.

• F: the ball floats in water.

• S: the game is rescheduled.

(CAS) => (R v F)

a. The game is canceled and rescheduled only if it rains or the ball floats in water.

b. The game is canceled and rescheduled if and only if it rains or the ball floats in water.

c. If the game is canceled and rescheduled, then either it rains or the ball floats in water.

d. If it rains or the ball floats in water, then the game is canceled and rescheduled.

QUESTION 14

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Tags:

mathematics

translation

formal language

formal logic

symbolic expression

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