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What is the cardinality of this set?
A={{ },{a,b}}
What is the cardinality of this set?
A={{ },{a,b}}
Suppose the domain of the propositional function P(x) consists of the integers −2,
−1, 0, 1, 2. Write out each of these propositions using disjunctions, conjunctions, and
negations.
a) ∃xP(x)
b) ∀xP(x)
c) ∃x¬P(x)
d) ∀x((x ≠ 1) → ¬P(x))
Suppose there are signs on the doors to two rooms. The sign on the first door reads “In this
room there is a lady, and in the other one there is a tiger”; and the sign on the second door
reads “In one of these rooms, there is a lady and in one of them there is a tiger.” Suppose
that you know that one these signs is true, and the other is false. Behind which door is the
lady? Explain your reasoning using propositions.
List the members of these sets.
{ x | x is a real number such that x2 = 1}
Given R is a relation from A = {1,2,3,4,5}, R={(1,1),(2,2),(2,3),(2,4),(3,3),(4,4),(4,5)}.
Is R an equivalence relation?
Calculate the total number of words that can be formed using the
letters of the word “MISSIPPI” if two ‘S’ and two ‘I’ are adjacent to
each other.
Construct a truth table for each of these compound propositions
(p ⊕ q) → (¬q ↔ r)
How many different strings can be made from the letters in the word rat?
A boy lives at X and wants to go to school at Z. From his home to X he has to first reach Y
and then Y to Z. He may go X to Y by either 3 bus routes or 2 train routes. From there, he can
either choose 4 bus routes or 5 train routes to reach Z. How many ways are there to go from X to
Z?
#340153 on Dec 2023