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Assign sentences to the letters to give these arguments obviously true premises and an ob false conclusion. a. If Athen B B Either Aor B B is not true. Example: If A then B A is not true So, B is not true Answer: A=Lyndon Johnson is president B=A Democrat is president

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CeciliaMaster · Tutor for 5 years

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\( A = \text{The sky is blue} \) \\ \( B = \text{2 + 2 = 4} \)

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To construct an argument with obviously true premises and an obviously false conclusion, we need to carefully select sentences for \( A \) and \( B \) such that the premises are true, but the conclusion is clearly false. Here, we will use logical constructs to achieve this. Given the premises: 1. If \( A \) then \( B \) 2. \( B \) 3. Either \( A \) or \( B \) And the conclusion: - \( B \) is not true We need to assign \( A \) and \( B \) such that: - The premises are true. - The conclusion is false. Let's choose: - \( A = \text{The sky is blue} \) - \( B = \text{2 + 2 = 4} \) Now, let's verify: 1. If the sky is blue, then \( 2 + 2 = 4 \) (True, because \( 2 + 2 = 4 \) is always true irrespective of the sky's color). 2. \( 2 + 2 = 4 \) (True). 3. Either the sky is blue or \( 2 + 2 = 4 \) (True, because \( 2 + 2 = 4 \) is always true). Conclusion: - \( 2 + 2 = 4 \) is not true (False, because \( 2 + 2 = 4 \) is always true).

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Assign sentences to the letters to give these arguments obviously true premises and an ob false conclusion. a. If Athen B B Either Aor B B is not true. Example: If A then B A is not true So, B is not true Answer: A=Lyndon Johnson is president B=A Democrat is president

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