Question

Let P and Q be statements: (a) Use truth tables to show that ∼ (P or...

Let P and Q be statements:

(a) Use truth tables to show that ∼ (P or Q) = (∼ P) and (∼ Q).

(b) Show that ∼ (P and Q) is logically equivalent to (∼ P) or (∼ Q).

(c) Summarize (in words) what we have learned from parts a and b.

Homework Answers

Answer #1

for (p or q) value , when both p and q are false then it will be false otherwise it is true .

For ( p and q) value , when both p and q are true then it will be true otherwise it is false .

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
Use two truth tables to show that the pair of compound statements are equivalent. p ∨...
Use two truth tables to show that the pair of compound statements are equivalent. p ∨ (q ∧ ~p); p ∨ q p q p ∨ (q ∧ ~p) T T ? ? ? ? ? T F ? ? ? ? ? F T ? ? ? ? ? F F ? ? ? ? ? p ∨ q T ? T T ? F F ? T F ? F
For three statements P, Q and R, use truth tables to verify the following. (a) (P...
For three statements P, Q and R, use truth tables to verify the following. (a) (P ⇒ Q) ∧ (P ⇒ R) ≡ P ⇒ (Q ∧ R). (c) (P ⇒ Q) ∨ (P ⇒ R) ≡ P ⇒ (Q ∨ R). (e) (P ⇒ Q) ∧ (Q ⇒ R) ≡ P ⇒ R.
are they logically equivalent (show how) truth table or in word:: a) p —> ( q...
are they logically equivalent (show how) truth table or in word:: a) p —> ( q —> r ) and ( p -> q) —> r b) p^ (q v r ) and ( p ^ q) v ( p ^ r )
Use a truth table to determine whether the two statements are equivalent. ~p->~q, q->p Construct a...
Use a truth table to determine whether the two statements are equivalent. ~p->~q, q->p Construct a truth table for ~p->~q Construct a truth table for q->p
1) Show that ¬p → (q → r) and q → (p ∨ r) are logically...
1) Show that ¬p → (q → r) and q → (p ∨ r) are logically equivalent. No truth table and please state what law you're using. Also, please write neat and clear. Thanks 2) .Show that (p ∨ q) ∧ (¬p ∨ r) → (q ∨ r) is a tautology. No truth table and please state what law you're using. Also, please write neat and clear.
Let A be a nonempty set and let P(x) and Q(x) be open statements. Consider the...
Let A be a nonempty set and let P(x) and Q(x) be open statements. Consider the two statements (i) ∀x ∈ A, [P(x)∨Q(x)] and (ii) [∀x ∈ A, P(x)]∨[∀x ∈ A, Q(x)]. Argue whether (i) and (ii) are (logically) equivalent or not. (Can you explain your answer mathematically and by giving examples in plain language ? In the latter, for example, A = {all the CU students}, P(x) : x has last name starting with a, b, ..., or h,...
(1) Determine whether the propositions p → (q ∨ ¬r) and (p ∧ ¬q) → ¬r...
(1) Determine whether the propositions p → (q ∨ ¬r) and (p ∧ ¬q) → ¬r are logically equivalent using either a truth table or laws of logic. (2) Let A, B and C be sets. If a is the proposition “x ∈ A”, b is the proposition “x ∈ B” and c is the proposition “x ∈ C”, write down a proposition involving a, b and c that is logically equivalentto“x∈A∪(B−C)”. (3) Consider the statement ∀x∃y¬P(x,y). Write down a...
Define a new logical connective ⋆ as follows: P ⋆ Q is true if P is...
Define a new logical connective ⋆ as follows: P ⋆ Q is true if P is false or Q is false. (That is, P ⋆ Q is only false if P and Q are both true.) Show that the operator ∼ (“not”) and the connectives ∨ (“or”), ∧ (“and”), and =⇒ (“if... then...”) can all be written in terms of ⋆ only. To get you started, ∼ P always has exactly the same truth value as (that is, is logically...
   Write a C++ program to generate all the truth tables needed for ( p ˄...
   Write a C++ program to generate all the truth tables needed for ( p ˄ q) ˅ (¬ p ˅ ( p ˄ ¬ q )). You need to submit your source code and a screen shot for the output
Show the following are not logically equivalent: ∀xP (x) ∨ ∀xQ(x) and ∀x(P (x) ∨ Q(x)).
Show the following are not logically equivalent: ∀xP (x) ∨ ∀xQ(x) and ∀x(P (x) ∨ Q(x)).
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT