Show that: (b) (p → q) → r and p →(q → r) are not logically equivalent.
6. Maximum score 3 ( 1 per part).
Show that:
(b) (p → q) → r and p →(q → r) are not logically equivalent.
(c) p ↔ q and ¬ p ↔ ¬ q are logically equivalent.
Homework Answers
1) First let us see what -> gives
p->q T when both are true or false and when q is true otherwise false.Hence based on this we have derived below truth table where we can see (p->q)->r and p->(q->r) are not logically equivalent.
| p | q | r | p->q | (p->q)->r | q->r | p->(q->r) |
| F | F | F | T | F | T | T |
| F | F | T | T | T | T | T |
| F | T | F | T | F | F | T |
| F | T | T | T | T | T | T |
| T | F | F | F | T | T | T |
| T | F | T | F | T | T | T |
| T | T | F | T | F | F | F |
| T | T | T | T | T | T | T |
2) P<-> Q shows bidirectional which means if and only if so when both false then true or when both true then true otherwise false, based on this we have below table to show they are logically equivalent
| p | q | p<->q | ~p | ~q | ~p <-> ~q |
| F | F | T | T | T | T |
| F | T | F | T | F | F |
| T | F | F | F | T | F |
| T | T | T | F | F | T |
Add Answer to:
Show that: (b) (p → q) → r and p →(q → r) are not logically equivalent.
How do you show the following propositions are logically equivalent? (a) [(p → q) → r]...
How do you show the following propositions are logically equivalent? (a) [(p → q) → r] ⊕ (p ∧ q ∧ r) and (p ∨ r) ⊕ (p ∧ q) (b) ¬∃x {P(x) → ∃y [Q(x, y) ⊕ R(x, y)] } and (∀x P(x)) ∧ [∀x ∀y(Q(x, y) ↔ R(x, y))] (c) Does [(p → q) ∧ (q → r)] → r implies (p → r) → r?
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.
Show that ~p -> (q -> r ) and q -> (p v r) are logically equivalent using laws
Show that ~p -> (q -> r) and q-> (p v r) are logically equivalent
WITHOUT constructing TT Show whether or not p-, q ^ (q-r)-p-, r is logically equivalent to
WITHOUT constructing TT Show whether or not p-, q ^ (q-r)-p-, r is logically equivalent to
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.
Question: Show that the propositions (p ∨ q) ∧ (¬p ∨ r) and (p ∧ r)...
Question: Show that the propositions (p ∨ q) ∧ (¬p ∨ r) and (p ∧ r) ⊕ (¬p ∧ q) are logically equivalent.
Show that negation \neg (p xor q) and p if and only if q are logically...
Show that negation \neg (p xor q) and p if and only if q are logically equivalent without using a truth
1. a) What is the truth value of (pvo) (pAo) when both p and q are b) Show-on 9) and-pwg are logically equivalent. c) Write the converse and contrapositive of the statement "If it is sunny, t...
1. a) What is the truth value of (pvo) (pAo) when both p and q are b) Show-on 9) and-pwg are logically equivalent. c) Write the converse and contrapositive of the statement "If it is sunny, then I will go swimming."
1. a) What is the truth value of (pvo) (pAo) when both p and q are b) Show-on 9) and-pwg are logically equivalent. c) Write the converse and contrapositive of the statement "If it is sunny, then I will...
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
Discrete math problems: 9. Show that p = 10. Show that p = q and (...
Discrete math problems:
9. Show that p = 10. Show that p = q and ( q p = n are logically equivalent. ) and q = (p V r) are logically equivalent. r
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.
WITHOUT constructing TT Show whether or not p-, q ^ (q-r)-p-, r is logically equivalent to
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.
1. a) What is the truth value of (pvo) (pAo) when both p and q are b) Show-on 9) and-pwg are logically equivalent. c) Write the converse and contrapositive of the statement "If it is sunny, then I will go swimming."
1. a) What is the truth value of (pvo) (pAo) when both p and q are b) Show-on 9) and-pwg are logically equivalent. c) Write the converse and contrapositive of the statement "If it is sunny, then I will...
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
Discrete math problems:
9. Show that p = 10. Show that p = q and ( q p = n are logically equivalent. ) and q = (p V r) are logically equivalent. r
Most questions answered within 3 hours.
-
8. What is the translational kinetic energy of a 0.1 g car
moving at 1 km/s?...
asked 57 seconds from now -
C++
Redo Practice program 1 from chapter 11, but this time define
the Money ADT class...
asked 18 minutes ago -
Experiment 7 Empirical Formula
Objectives:
Determine the expected formula for the ionic oxide expected
when Mg...
asked 27 minutes ago -
When aqueous solutions of NH4OH(aq)
and CuCl2(aq) are mixed, the products
are NH4Cl (aq) and
Cu(OH)2(s)....
asked 30 minutes ago -
Describe the heart of different animals in circulation and
explain.
Fish 2 chambered Heart.
Amphibians 3...
asked 38 minutes ago -
Which has the greater rotational momentum, the disc or the
ring?
asked 41 minutes ago -
____ is a solid that contains hydrocarbons of high molecular
weight as well as compounds containing...
asked 44 minutes ago -
Hendrix & Franks Company had the following beginning and
ending inventory balances for the current year...
asked 45 minutes ago -
2. For each of the following predict the product(s) of the
reaction, write the net ionic...
asked 42 minutes ago -
(1) Prompt the user to input a wall's height and width.
Calculate and output the wall's...
asked 46 minutes ago -
Question 2: (1 point)
Suppose that A and B react to form C according to the...
asked 48 minutes ago -
The antacid Brioschi, which has been used to relieve heartburn,
is mainly sodium bicarbonate. Predict the...
asked 59 minutes ago