In November 2024
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Minimise the following DNFs using
(a) Karnaugh maps
(b) Quine-McCluskey method
1. x y z ∨ x y z' ∨ x y' z ∨ x y' z' ∨ x' y z ∨ x' y' z ∨ x' y' z'
2. x y z' ∨ x y' z' ∨ x' y' z ∨ x' y' z'.
Let P(x, y) be the statement "x takes y ", where the domain for x consists of all people and y consists of train to work.
a Everyone takes train to work.
b There is someone who took train to work.
c There is someone who took at least one train to work.
d Everyone takes at least one train to work.
e Someone takes at least one train to work.
- Let P(x, y) be the statement "pupil x has taken class y", where the domain for x consists of pupils and y consists of Discrete Mathematics. Express each of the quantification in English sentences.
a.∀x∀y P(x, y)
b∀x∃y P(x, y)
c∃x∃y P(x, y)
d∃x∀y P(x, y)
F(n) = n^3 onto function
1.4 If Universal Set U = {90, 91 , 92 , 93 , 94, 95 , 96 , 97 , 98, 99 , 100} (10)
A = {90, 92, 94, 96, 98, 100},
B= {91, 93, 95, 97, 99},
C = {90, 94, 98}
1.4.1 What is (A ∩ C)c
1.4.2 What is(B ∪ C)c
Show the behaviour of the circuit below using a Truth table (￢𝑝 ∨ ￢𝑞) ∧ (𝑝 ∨ 𝑟)
3 Using a Truth table, determine the value of the compound proposition
((𝑝 ∨ 𝑞) ∧ (￢𝑝 ∨ 𝑟)) → (𝑞 ∨ 𝑟).
Determine whether ( 𝑝∨𝑞)∧(𝑝→𝑟)∧( 𝑞→𝑠)→𝑟∨𝑠 is a Tautology or a contradiction
.List all subsets of{ , , , , },containing but not containing
List all subsets of{0,1,3}.How many do you get?
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#340153 on Dec 2023