First diagram the following statements; then, using the until tables for negatio

Question

First diagram the following statements; then, using the until tables for negation, disjunction, conjunction, and conditional (material implication truth table), tell whether each one is true or false. (You will have to use knowledge of the real world as well as your knowledge of the truth tables) a. Either Barack Obama was elected president of the United States in 2008 or the chickadee is the national bird of the United States. B G B is true, C is false; thus (by the second line of the truth-functional definition of disjunction) the statement is true. b. If Venus is the largest planet in the solar system, then there is intelligent life elsewhere in our universe. V rightarrow I(I stands for there is intelligent life elsewhere in our universe). The antecedent is false (Jupiter is largest). Is the consequent true, or is it false? Who knows? But for our purposes, who cares? We don't need to know; since we already know that the conditional statement must be true: Since the antecedent is false, the statement will be true no matter what the truth value of the consequent. Orange juice contains vitamin G and baseball is played with a round ball. If some apples are red, then the Earth is flat. Either the Earth is flat or Barcelona is in Spain. If the Earth is flat, then all apples are orange.

Explanation / Answer

1. Let O = represent orange juice contains vitain C

and B = baseball is played with a round ball.

O B , O and B are true as orange does contain vitamin C and baseball is round in shape.

Hence the statement is true by the conjunction rule.

conjunction is a compound sentence formed by using the word and to join two simple sentences.

2. Let A denote if some apples are red

and E denote Earth is flat

A --> E . THis is true

its true that some apples are red . although th earth is not flat its somewhat round but since the conditional statement is true

that is ''if some apples are red'' so its not important whether the consequent that is E is true or false.

3. Let E denote either the earth is flat

and B denote Barcelona is in Spain

E V B , this is true

We know that the earth is not flat so E is false but we are pretty sure that Barcelona is in Spain so B is true.

So by definition of disjunction E V B is true .

Here we need atleast any of the two statements to be true and the entire statement will be true.

4.Let E denote if the earth is flat

and A denote all apples are oranges

E   --> A , this statement is false as the conditional statement that is represented by E is false

we know that the Earth is not a perfect sphere but it for sure not flat.

THe consequent is false. But we only need to worry about the conditional statement

=> THis is false by the definition of conditional statement.

Related Questions

Navigate

• Browse (All)
• Browse F
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.