Search & Filtering
1. Determine whether this proposition is a tautology.
[(p → q) ∧ (q → r)] → (p→ r)
Determine whether this proposition is a tautology.
[(p → q) Ù (q → r)] → (p→ r)
What is the value of this statement -B if B = F.
A. True
B. False
What is the value of this statement -(B VC) if B=F.C=T.
A. True
B. False
What is the value of this implication p→qif p = F and q = F.
A. True
B. False
Define permutation function and find out all permutation on the set S = {𝑎, 𝑏, 𝑐}
Define a characteristic function on a set 𝑆 on a universal set 𝑈 and prove that
𝑓𝐴∩𝐵(x) = 𝑓𝐴(x) . 𝑓𝐵(x)
Determine whether each of the function from 𝑍 to Z is onto
(a) 𝑓(𝑛) = 𝑛³
(b) 𝑓(𝑛) = 𝑛² − 1
Determine whether each of the function from 𝑍 to Z is one to one
(a) 𝑓(𝑛) = 𝑛 − 1
(b) 𝑓(𝑛) = 𝑛² + 1
Let 𝐴 and 𝐵 be sets such that 𝐴 ∪ 𝐵 ⊆ 𝐵 and 𝐵 ⊆ 𝐴 . Draw the corresponding Venn
diagram
Determine whether each of the following statement is true or false. Briefly explain your
answer.
(a) ∅ ⊆ ∅ (b) ∅ ∈ ∅ (c) ∅ ⊆ {∅} (d) ∅ ∈ {∅}
(e) {𝑎, 𝑏} ⊆ {𝑎, 𝑏, 𝑐,{𝑎, 𝑏, 𝑐}} (f) {𝑎, ∅} ∈ {𝑎,{𝑎, ∅}}
