Consider the following:F → (B ∨ A)D → F¬(B ∨ A)..∴ ¬(D ∧ C)Which of the following can be derived from the premises?¬B ∨ ¬A¬(D ∨ C)¬B ∧ ¬A¬D
Question
Consider the following:
F → (B ∨ A)
D → F
¬(B ∨ A)
..
∴ ¬(D ∧ C)
Which of the following can be derived from the premises?
- ¬B ∨ ¬A
- ¬(D ∨ C)
- ¬B ∧ ¬A
- ¬D
Solution
The premises are:
- F → (B ∨ A)
- D → F
- ¬(B ∨ A)
We are asked to derive: ¬(D ∧ C)
Let's go step by step:
From the third premise, we know that neither B nor A is true.
From the first premise, if F were true, then B or A would be true, which contradicts our third premise. Therefore, F must be false.
From the second premise, if D were true, then F would be true, which contradicts our conclusion that F is false. Therefore, D must be false.
Therefore, ¬D is true.
However, we don't have any information about C. So, we can't make any conclusions about ¬C or C
Similar Questions
_ _ _ _ _ _ _ _ _ _ _ TC13: 9*∀z (h(z) ∧ s(z)) → ∃z m(z)h(y) → m(y)∀x(h(x) → m(x))h(y) ∧ s(y) → m(y)¬h(y) ∨ m(y)¬(h(y) ∧ s(y)) ∨ m(y)
Using Boolean laws simplify each of the following propositions:a. a ∧ b ∨ a ∧ ¬b
Show that ¬(𝑝 ∨ (¬𝑝 ∧ 𝑞)) and ¬𝑝 ∧ ¬𝑞 are logically equivalent by:a) Using a truth table (3 POINTS)b) Using logical equivalences
Which of the following is a contradiction?(p∧q)∧~(p∨q)p∨(~p∧q)(p⇒q)⇒pNone of these
De Morgan's law is used in finding the equivalence of a logic expression using other logical functions.Question 11Select one:TrueFalse
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.