Archangel Macsika
Write CONVERSE of the following statements. a)If P is a square, then P is a rectangle. b)If n is prime, then n is odd or n is 2. c)If Aangloo is Meena's father, then Baangloo is her uncle and Bingli is her Aunt. d)A positive integer is prime only if it has no divisors other than 1 and itself. e)Being divisible by 3 is a necessary condition for this number to be divisible by 9.
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Here's the Solution to this Question
(a) If P is a square, then P is a rectangle.
Let Q be “P is a square” and R be “P is a rectangle.” Then we have:
Original: Q → R
=∼ Q ∨ R
Negation: ∼ (∼ Q ∨ R)
= Q ∧ ∼ R
Which translates to P is a square and not a rectangle.
Converse:
R → Q
Which translates to If P is a rectangle, then P is a square.
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(b) If n is prime, then n is odd or n is 2. Let Q be “n is prime” and R be “n is odd or n is 2.”
Then we have:
Original: Q → R =∼Q∨R
Negation: ∼ (∼ Q∨R) =Q∧∼R
If we negate R, we have:
∼(n is odd∨n is 2) =∼(n is odd) ∧ ∼ (n is 2)
Which translates to n is even and n is not 2.
Converse: If n is odd or n is 2, then n is prime.
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(c) If aangloo is meena’s father, then Baangloo is her uncle and bingli is her aunt.
Let Q be “aangloo is meena's father” and R be “baangloo is her uncle and bingli is her aunt.”
Then, as before
∼(Q→R)=Q∧∼R
If we negate R, we have:
∼(baangloo is her uncle ∧bingli is her aunt) ∼(baangloo is her uncle) ∨ ∼ (bingli is her aunt)
Which translates to baangloo is not her uncle or bingli is not her aunt. Negation: aangloo is meena's father and either baangloo is not her uncle or bingli is not her aunt.
Converse: If baangloo is her uncle and bingli is her aunt, then aangloo is meena's father.
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(d)
Let ,
p: A positive interger is a prime
q: Has no divisor other than 1 and itself.
Converse
q → p
A positive integer is a prime if it has no divisors other than 1 and itself.
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(e)
let
p:this number divisible by 3
q:this number to be divisible by 9.
Converse
q → p
this number divisible by 3 if this number to be divisible by 9.