Flashcards · 8 cards

Sets & logic

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Rule
$(A \cup B)' = \,?$
Answer
$A' \cap B'$ : outside the union means in neither set.
(A ∪ B)′ = A′ ∩ B′outside the union: in neither set
From the lesson: Sets and logic
Rule
$(A \cap B)' = \,?$
Answer
$A' \cup B'$ : not in both means outside at least one.
(A ∩ B)′ = A′ ∪ B′not in both: outside at least one
From the lesson: Sets and logic
Know it
$n(A \cup B) = \,?$
Answer
$n(A) + n(B) - n(A \cap B)$ .
From the lesson: Sets and logic
Rule
When is $p \wedge q$ true?
Answer
Only when both are true.
p q p ∧ q
T T T
T F F
F T F
F F F
p ∧ qTrue only when both are true
From the lesson: Sets and logic
Rule
When is $p \vee q$ false?
Answer
Only when both are false.
p q p ∨ q
T T T
T F T
F T T
F F F
p ∨ qFalse only when both are false
From the lesson: Sets and logic
Rule
When is $p \Rightarrow q$ false?
Answer
Only when $p$ is true and $q$ is false.
p q p ⇒ q
T T T
T F F
F T T
F F T
p ⇒ qFalse only when p is true and q is false
From the lesson: Sets and logic
Rule
When is $p \Leftrightarrow q$ true?
Answer
When $p$ and $q$ match.
p q p ⇔ q
T T T
T F F
F T F
F F T
p ⇔ qTrue when p and q match
From the lesson: Sets and logic
Which method?
NECO 2023 · Paper 2 · Q1
Let $U = \{e, f, g, h, i\}$ be a universal set, and $X = \{e, g\}$ and $Y = \{g, h\}$ subsets of $U$ .
Draw a Venn diagram to represent the information.
Use the Venn diagram to find (i) $X'$ ; (ii) $(X \cup Y)'$ ; (iii) $X' \cap Y'$ .
How can (b)(ii) and (b)(iii) be checked against each other?
Answer
Place each element once in the Venn diagram. $(X \cup Y)'$ is what lies outside both circles, and by De Morgan's law $X' \cap Y'$ is the same set.
From the lesson: Sets and logic Try the question

p	q	p ∧ q
T	T	T
T	F	F
F	T	F
F	F	F

p	q	p ∨ q
T	T	T
T	F	T
F	T	T
F	F	F

p	q	p ⇒ q
T	T	T
T	F	F
F	T	T
F	F	T

p	q	p ⇔ q
T	T	T
T	F	F
F	T	F
F	F	T