Identify the converse of the statement R → S: "If it rains, then he will stay home." Question 6 options:

A)

∼R → ∼S: If it doesn't rain, then he won't stay home.

B)

∼R → S: If it doesn't rain, then he will stay home.

C)

S → R: If he stays home, then it will rain.

D)

R ↔ S It will rain if and only if he stays home.

The correct option C:

C) S → R: If he stays home, then it will rain.

Step-by-step explanation:

There are three main transformation for an if-then statements. These three are names are converse, inverse and contrapositive.

If the statement is given:

R → S: "If it rains, then he will stay home."

Then its Converse will be:

S → R: If he stays home, then it will rain.

Its Inverse will be:

∼R → ∼S: If it doesn't rain, then he won't stay home.

Its Contrapositive will be the inverse of the converse.

yes

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step-by-step explanation:

option a, c,d are correct.

step-by-step explanation:

from the given figure, it is given that z is equidistant from the sides of the triangle rst, then from triangle tzb and triangle szb, we have

tz=sz(given)

bz=zb(common)

therefore, by rhs rule,δtzb ≅δszb

by cpctc, sz≅tz

also, from δctz and δasz,

tz=sz(given)

∠tcz=∠saz(90°)

by rhs rule, δctz ≅ δasz, therefore by cpctc, ∠ctz≅∠asz

also,from δasz and δzsb,

zs=sz(common)

∠zbs=∠saz=90°

by rhs rule, δasz ≅δzsb, therefore, by cpctc, ∠asz≅∠zsb

hence, option a, c,d are correct.