Let's go through each of these logical statements one by one: a. False |= True: This statement is saying that False implies True. In logic, this is actually considered to be True. So, this statement is True. b. True |= False: This statement is saying that True implies False. In logic, this is considered to be False. So, this statement is False. c. (A^B) |= (AB): This statement is saying that (A and B) implies (A if and only if B). This is not always true. For example, if A is True and B is False, then (A and B) is False, but (A if and only if B) is also False. So, this statement is False. d. AB |= AvB: This statement is saying that (A if and only if B) implies (A or B). This is always true. If A is equivalent to B, then either both are true or both are false. In either case, (A or B) is true. So, this statement is True. e. AB |= -AvB: This statement is saying that (A if and only if B) implies (not A or B). This is not always true. For example, if A is True and B is True, then (A if and only if B) is True, but (not A or B) is False. So, this statement is False. So, the true logical statements are a and d.

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Let's go through each of these logical statements one by one: a. False |= True: This statement is saying that False implies True. In logic, this is actually considered to be True. So, this statement is True. b. True |= False: This statement is saying that True implies False. In logic, this is considered to be False. So, this statement is False. c. (A^B) |= (A<=>B): This statement is saying that (A and B) implies (A if and only if B). This is not always true. For example, if A is True and B is False, then (A and B) is False, but (A if and only if B) is also False. So, this statement is False. d. A<=>B |= AvB: This statement is saying that (A if and only if B) implies (A or B). This is always true. If A is equivalent to B, then either both are true or both are false. In either case, (A or B) is true. So, this statement is True. e. A<=>B |= -AvB: This statement is saying that (A if and only if B) implies (not A or B). This is not always true. For example, if A is True and B is True, then (A if and only if B) is True, but (not A or B) is False. So, this statement is False. So, the true logical statements are a and d.

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Let's go through each of these logical statements one by one: a. False |= True: This statement is saying that False implies True. In logic, this is actually considered to be True. So, this statement is True. b. True |= False: This statement is saying that True implies False. In logic, this is considered to be False. So, this statement is False. c. (A^B) |= (A<=>B): This statement is saying that (A and B) implies (A if and only if B). This is not always true. For example, if A is True and B is False, then (A and B) is False, but (A if and only if B) is also False. So, this statement is False. d. A<=>B |= AvB: This statement is saying that (A if and only if B) implies (A or B). This is always true. If A is equivalent to B, then either both are true or both are false. In either case, (A or B) is true. So, this statement is True. e. A<=>B |= -AvB: This statement is saying that (A if and only if B) implies (not A or B). This is not always true. For example, if A is True and B is True, then (A if and only if B) is True, but (not A or B) is False. So, this statement is False. So, the true logical statements are a and d.

Which of the following logical statements is true? a. False |= True b. True |= False c. (A^B) |= (A<=>B) d. A<=>B |= AvB e. A<=>B |= -AvB

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Which of the following logical statements is true?

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