Let p and be logical statements. By using a truth table determine if the following compound statements are logically equivalent
Problem 12.1: Let p and be logical statements. By using a truth table determine if the following compound statements are logically equivalent. Show work!
Circle one:
A: The statements are equivalent. B: The statements are not equivalent.
Problem 12.2: Let P, Q, and be be logical statements. By using a truth table determine if the following compound statements are logically equivalent. Show work!
Circle one: A:
The statements are equivalent. B: The statements are not equivalent.
Homework Answers
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Let p and be logical statements. By using a truth table determine if the following compound statements are logically equivalent
4. Use truth tables to determine whether the following two statements are logically equivalent. (P+Q)^(~Q) and...
4. Use truth tables to determine whether the following two statements are logically equivalent. (P+Q)^(~Q) and ~ (PVQ)
4. (8 Points) Using a truth table, prove the following statements are logically equivalent. Be sure...
4. (8 Points) Using a truth table, prove the following statements are logically equivalent. Be sure to include an explanation of how your truth table demonstrates this conclusion. -(X VY)= -X A-Y
5 points Show that p + (q + r) and q + (pvr) are logically equivalent...
5 points Show that p + (q + r) and q + (pvr) are logically equivalent without using a truth table. To get full credit, include which logical equivalences you used.
2. (a) Show that (PVQ) + R is not logically equivalent to (P + R) V(Q...
2. (a) Show that (PVQ) + R is not logically equivalent to (P + R) V(Q + R) using a truth table. (b) Is (PAQ) → R logically equivalent to (P + R) A( Q R )? If so, use a truth table to establish this. If not, show that it is false.
5.) Logic problems. List the truth values of the two statements of problems (a) and the...
5.) Logic problems. List the truth values of the two statements
of problems
(a) and the truth value of the statement of problem (b) in terms of
the truth
values of P and Q.
a.) Determine if the following pairs of logical statements are
equivalent.
Show why they are or are not equivalent.
i. (( P) ^ Q) ) P;
ii. (P _ ( Q)):
b.) Determine if the following statement is a tautology. Show why
it is
or is...
Use a truth table to determine whether the two statements are equivalent. (-p-9)^(-→-p) and -- Complete...
Use a truth table to determine whether the two statements are equivalent. (-p-9)^(-→-p) and -- Complete the truth table. р т q-p-9A(---)-P4-9 T T F T F F F Choose the correct answer below. о The statements are equivalent. The statements are not equivalent. O
QUESTION 2 a. Let p and q be the statements. i Construct the truth table for...
QUESTION 2 a. Let p and q be the statements. i Construct the truth table for (-p V q) ^ q and (-p) v q. What do you notice about the truth tables? Based on this result, a creative student concludes that you can always interchange V and A without changing the truth table. Is the student, right? ii. Construct the truth tables for (-p VG) A p and (-p) v p. What do you think of the rule formulated...
Is the following sentence a logical truth, inconsistency, or contingency? Provide a truth table: ¬ (P...
Is the following sentence a logical truth, inconsistency, or contingency? Provide a truth table: ¬ (P → (¬P ∧ Q)) ∨ (Q → P)
Assume that p NAND q is logically equivalent to ¬(p ∧ q). Then, (a) prove that...
Assume that p NAND q is logically equivalent to ¬(p ∧ q). Then, (a) prove that {NAND} is functionally complete, i.e., any propositional formula is equivalent to one whose only connective is NAND. Now, (b) prove that any propositional formula is equivalent to one whose only connectives are XOR and AND, along with the constant TRUE. Prove these using a series of logical equivalences.
Discrete Math: Decide whether (p^q)r and (pr)^(qr) are logically equivalent using boolean algebra. Show work! Do...
Discrete Math:
Decide whether (p^q)r and
(pr)^(qr) are
logically equivalent using boolean algebra. Show work! Do NOT use
truth table.
We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this image
4. Use truth tables to determine whether the following two statements are logically equivalent. (P+Q)^(~Q) and ~ (PVQ)
4. (8 Points) Using a truth table, prove the following statements are logically equivalent. Be sure to include an explanation of how your truth table demonstrates this conclusion. -(X VY)= -X A-Y
5 points Show that p + (q + r) and q + (pvr) are logically equivalent without using a truth table. To get full credit, include which logical equivalences you used.
2. (a) Show that (PVQ) + R is not logically equivalent to (P + R) V(Q + R) using a truth table. (b) Is (PAQ) → R logically equivalent to (P + R) A( Q R )? If so, use a truth table to establish this. If not, show that it is false.
5.) Logic problems. List the truth values of the two statements
of problems
(a) and the truth value of the statement of problem (b) in terms of
the truth
values of P and Q.
a.) Determine if the following pairs of logical statements are
equivalent.
Show why they are or are not equivalent.
i. (( P) ^ Q) ) P;
ii. (P _ ( Q)):
b.) Determine if the following statement is a tautology. Show why
it is
or is...
Use a truth table to determine whether the two statements are equivalent. (-p-9)^(-→-p) and -- Complete the truth table. р т q-p-9A(---)-P4-9 T T F T F F F Choose the correct answer below. о The statements are equivalent. The statements are not equivalent. O
QUESTION 2 a. Let p and q be the statements. i Construct the truth table for (-p V q) ^ q and (-p) v q. What do you notice about the truth tables? Based on this result, a creative student concludes that you can always interchange V and A without changing the truth table. Is the student, right? ii. Construct the truth tables for (-p VG) A p and (-p) v p. What do you think of the rule formulated...
Discrete Math:
Decide whether (p^q)r and
(pr)^(qr) are
logically equivalent using boolean algebra. Show work! Do NOT use
truth table.
We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this image
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