(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...
2.
a. In what order are the operations in the following propositions
performed? i. P ∨ ...
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...
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...
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...
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?