Question

Are the statement forms P∨((Q∧R)∨ S) and ¬((¬ P)∧(¬(Q∧ R)∧ (¬ S))) logically equivalent? I found that they were not logically equivalent but wanted to check. Also, does the negation outside the parenthesis on the second statement form cancel out with the negation in front of P and in front of (Q∧ R)∧ (¬ S)) ?

Answer #1

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.

(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...

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 )

Discrete Math
1. Write the compound statements in disjunctive
normal form. (Since they are logically equivalent, they have the
same disjunctive normal form, so you only need to give one
answer.
(p → q) ∧ (¬r → q) and (p ∨ ¬r) → q
2. Consider the premises:
• It is not snowing today and it is windy;
• School will be canceled only if it is snowing today;
• If school is not canceled today, then our study group will...

Let p, q, and r represent the following simple statements.
p:
It is snowing outside
q:
It is cold
r:
It is cloudy.
Write the following compound statement in its symbolic form.
If
it is snowing outside
then
it is cold
or
it is not cloudy

2.
a. In what order are the operations in the following propositions
performed? i. P ∨ ¬q ∨ r ∧ ¬p
ii. P ∧ ¬q ∧ r ∧ ¬p iii. p ↔ q
∧ r → s b. Suppose that x is a proposition generated by
p, q, and r that is equivalent to p ∨ ¬q. Write out x
as a function of p, q, and r, and then give the truth table for
x

2. Let A = {p, q, r, s}, B = {k, l, m, n}, and C = {u, v, w},
Define f : A→B by f(p) = m, f(q) = k, f(r) = l, and f(s) = n, and
define g : B→C by g(k) = v, g(l) = w, g(m) = u, and g(n) = w. Also
define h : A→C by h = g ◦ f. (a) Write out the values of h. (b) Why
is it that...

Kari has identified three loci, Q, R, S, found in order on the q
arm of a pair of homologous chromosomes. In recent experiments, she
has generated a triple heterozygote from a triple dominant parent
(QQRRSS) and a triple recessive parent (qqrrss). a) Sketch the
arrangement of the alleles on each homologue after the chromosomes
have condensed, but before any crossing over has occurred. b) Name
the possible genotypes of a gamete derived from a chromatid for
which no homologous...

Consider permutations of the 26-character lowercase alphabet
Σ={a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r,s,t,u,v,w,x,y,z}.
In how many of these permutations do
a,b,c occur consecutively and in that
order?
In how many of these permutations does a appear before
b and b appear before c?

Labor Relations- Chapter 5- G o v e r n m e n t s , L a b o u r
R e l a t i o n s B o a r d s , a n d O t h e r P a r t i e s
Case Study- Quality Inn & Suites Brantford v. UFCW Local
175
In January 2012 the Ontario Labour Relations Board was asked to
consider an application for the...

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