(1) For each assertion below, indicate if it is true (T) or false (F) by circlin
ID: 3586029 • Letter: #
Question
(1) For each assertion below, indicate if it is true (T) or false (F) by circling the correct response.
(a) (T, F) The statement, “this statement is false” is a proposition.
(b) (T, F) The statement “If I am Spider-Man, then I can breath in space” is true.
(c) (T, F) The statement “Spider-Man can breath in space” is true.
(d) (T, F) “F p” can be false.
(e) (T, F) “The proposition p ¬p is not satisfiable.
(f) (T, F) The proposition p q has the same truth value as ¬q ¬p.
(g) (T, F) p q ¬p q is a tautology.
(h) (T, F) x(P(x) Q(x)) xP(x) xQ(x) is a tautology.
(i) (T, F) x(P(x) Q(x)) xP(x) xQ(x) is a tautology.
(j) (T, F) If U = Z + then nm(n 2 < m) is true.
(k) (T, F) If U = Z + then mn(n 2 < m) is true.
(l) (T, F) If U = R then x(0 < x < 1).
(m) (T, F) If U = Z then x(0 < x < 1).
(n) (T, F) 6= {}.
(o) (T, F) {0, 1} {0, {1}}.
(p) (T, F) {0, 1} {0, {0, 1}}.
(q) (T, F) {{}} / .
(r) (T, F) {a, b} {a, a, b}.
(s) (T, F) {a} {a, b, {a, b}}.
(t) (T, F) b {a, {a, b}}.
Explanation / Answer
Please see the below answer.
Answer:
Answer:
a) If the statement is false then it is false that this sentence is (False),
b) The statement “If I am Spider-Man, then I can breath in space” is true. ( T) . As True + true = (True).
c)The statement “Spider-Man can breath in space” is true. (False)
d)“F p” can be false. If F is true and p is false , then False (True)
e)“The proposition p ¬p is not satisfiable .If p is true and ¬p is false or ¬p is true and p is false, then (False ).
f)The proposition p q has the same truth value as ¬q ¬p.(True). Same truth table
g)p q ¬p q is a tautology.(True)
h)x(P(x) Q(x)) xP(x) xQ(x) is a tautology. (False), Because x(P(x) Q(x)) xP(x) xQ(x) is a tautology.
i) x(P(x) Q(x)) xP(x) xQ(x) is a tautology. (False)
j) If U = Z + (Z + set of positive integer greater than 0) then nm(n 2 < m) is true. (True)
k) If U = Z + (Z + set of positive integer greater than 0) then mn(n 2 < m) is true. (False)
l) If U = R (R i.e set of real numbers) then x(0 < x < 1).(True)
m) If U = Z (Z i.e set of integers)then x(0 < x < 1). (False)
n) 6= {}.(False) because or {} is empty set with cardinality 0 as finite set, so that 6 {1,2,3,..}
o) {0, 1} {0, {1}}. (False)
p) {0, 1} {0, {0, 1}}.( True)
q) {{}} /. Undefined (False)
r) {a, b} {a, a, b}. (False) as does not hold condition of proper subset because both have same elements a,b
s) {a} {a, b, {a, b}}. (True) as a belongs to {a,b,{a,b}}
t) b {a, {a, b}}. (True) as b belongs to {a,{a,b}}
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