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Given the following 2 premises, 1. 𝑝 → (𝑞 ∨ 𝑟) 2. 𝑞 → 𝑠 Prove 𝑝 → (𝑟 ∨ 𝑠) is valid using the Proof by Contradiction method.
F. How many different sequences, each of length r, can be formed using elements
from A if
(a) elements in the sequence may be repeated?
(b) all elements in the sequence must be distinct?
F. Show using the rules of resolution/inference, that no
single assignment of truth values to p, q, r makes all
the disjunctions p V-9, p V-9,9 V r,
qVT, V revaluate to true. Proof using truth
na
Show that the following logical equivalences hold for the
Peirce arrow ↓, where P ↓ Q ≡ ∼(P ∨ Q).
a. ∼P ≡ P ↓ P
b. P ∨ Q ≡ (P ↓ Q) ↓ (P ↓ Q)
c. P ∧ Q ≡ (P ↓ P) ↓ (Q ↓ Q)
H d. Write P → Q using Peirce arrows only.
e. Write P ↔ Q using Peirce arrows only.
F. Define and give examples of injective surjective and bijective functions. Check the injectivity and surjectivity of the following function f: NN given by f(x)=x2
Prove that the relation R:{(x,y)|x-y is divisible by 3} is an Equivalence relation.(R is
defined over Z) L2 CO2 10
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#339914 on Dec 2023