Question

Consider the following propositional formula: (((A ^ B) -> C) ^ ((A ^ C) -> D))...

Consider the following propositional formula:

(((A ^ B) -> C) ^ ((A ^ C) -> D)) -> ((A ^ B) -> D)

Perform the following tasks for this formula:

Use the truth-table method to determine if this formula is valid, satisfiable, or unsatisfiable. Show all your work.

Homework Answers

Answer #1

VALID since all are 'T's only.

To be simple, shown the Truth values for each operator.

Please up vote. I need it very badly right now. Comment if you have any doubts. Happy Learning!

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Consider the following propositional formula: ((A ^ B) -> C) ^ (A ^ C -> D))...
Consider the following propositional formula: ((A ^ B) -> C) ^ (A ^ C -> D)) -> ((A ^ B) -> D) Perform the following task for this formula: Convert this formula into CNF form and write a numbered list of all clauses obtained from this formula. Use the truth-table method to determine if this formula is valid, satisfiable, or unsatisfiable.
3. Consider the following argument: If there is free food outside, it is a sunny day....
3. Consider the following argument: If there is free food outside, it is a sunny day. I am in class if there was no free food outside. Therefore, I am in class while it is not sunny out. (a) Translate this argument into formal logical notation. Carefully define the propositional variables you use. (b) Use a truth table to determine whether the argument is valid or invalid. Explain how your table shows that the argument is valid/invalid.
Use a truth table or the short-cut method to determine if the following set of propositional...
Use a truth table or the short-cut method to determine if the following set of propositional forms is consistent:   { ¬ p ∨ ¬ q ∨ ¬ r, q ∨ ¬ r ∨ s, p ∨ r ∨ ¬ s, ¬ q ∨ r ∨ ¬ s, p ∧ q ∧ ¬ r ∧ s }
Use the FULL truth-table method to determine whether the following argument form is valid or invalid....
Use the FULL truth-table method to determine whether the following argument form is valid or invalid. Show the complete table (with a column of ‘T’s and ‘F’s under every operator); state explicitly whether the argument form is valid or invalid; and clearly identify counterexample rows, if there are any. (p ⋅ q) ⊃ ~(q ∨ p), p ⊃ (p ⊃ q) /∴ q ≡ p Use the FULL truth-table method to determine whether the following argument form is valid or...
Consider the following mechanism. 2A <-----> B+C Equillibrium B+D-----> C Slow ---------------------------------- 2A+D-----------> C+E Determine the...
Consider the following mechanism. 2A <-----> B+C Equillibrium B+D-----> C Slow ---------------------------------- 2A+D-----------> C+E Determine the rate law
Write the truth table for the following expression f (a, b, c, d) = ∑m (1,6,5,3,7,4)...
Write the truth table for the following expression f (a, b, c, d) = ∑m (1,6,5,3,7,4) And the conditions do not matter are d (a, b, c, d) = ∑d (10,13,14)
Consider the following Boolean expression (a + b) . (a + c). Provide a simpler expression...
Consider the following Boolean expression (a + b) . (a + c). Provide a simpler expression (fewer gates) that is equivalent. Show that your expression is equivalent by building truth tables for both expressions in the same way as we've done before. 1a. Imagine that you have designed a circuit that uses N expressions of the form (a + b) . (a + c). We replace each of these with your solution to question 1. How many fewer transistors will...
#9) You are to implement the following function F(A,B,C,D,E,F) which outputs a 1 whenever the binary...
#9) You are to implement the following function F(A,B,C,D,E,F) which outputs a 1 whenever the binary number represented by ABCDE is ODD and 0 otherwise. A is the MSB and E is the LSB. Draw the function F(A,B,C,D,E,F) and show the work that led you to that answer. Since I am not so sadistic as to have you draw the truth table of a 6 variable function and draw the K-map of such a function, you should realize, as a...
1. There are three islanders: A says “If B and I are both telling the truth,...
1. There are three islanders: A says “If B and I are both telling the truth, then so is C”, B says “If C is telling the truth, then A is lying”, and C says “It is not the case that all three of us are telling the truth.” Using propositional variables a, b, and c to represent the truth of the statements of A, B, and C respectively, we can represent the problem by the three premises a ↔...
Consider the following bivariate data. Point A B C D E F G H I J...
Consider the following bivariate data. Point A B C D E F G H I J x 0 1 1 2 3 4 5 6 6 7 y 5 5 8 3 4 1 2 0 1 1 (a) Construct a scatter diagram of the given bivariate data. (Do this on paper. Your instructor may ask you to turn in this work.) (b) Calculate the covariance. (Give your answer correct to two decimal places.) (c) Calculate sx and sy. (Give...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT