Lewis carroll's puzzle in terms of axioms.

lewis carroll axiom 1. if a kitten loves fish, then it is teachable

lewis carroll axiom 2. every kitten without a tail will play with a gorilla

lewis carroll axiom 3. all kittens with whiskers love fish

lewis carroll axiom 4. if a kitten has green eyes, then it is not teachable

lewis carroll axiom 5. all kittens have whiskers or do not have tails.

now, prove the following statements using only the axioms given above.

statement 7.11 if a kitten has a tail, then it does not have green eyes.

statement 7.10 if a kitten has green eyes, then it does not love fish.

write the proof to justify the statement.

Step-by-step explanation:

Consider the provided information.

Lewis Carroll Axiom 1. If a kitten loves fish, then it is teachable

Lewis Carroll Axiom 2. Every kitten without a tail will play with a gorilla

Lewis Carroll Axiom 3. All kittens with whiskers love fish

Lewis Carroll Axiom 4. If a kitten has green eyes, then it is not teachable

Lewis Carroll Axiom 5. All kittens have whiskers or do not have tails.

Statement 7.11 If a kitten has a tail, then it does not have green eyes.

From Axiom 5 All kittens have whiskers or do not have tails.

It is given that kitten has tail so it must whiskers.

From Axiom 3 All kittens with whiskers love fish .

That means If a kitten has a tail it will whiskers and love fish.

From Axioms 1 If a kitten loves fish, then it is teachable .

That means kitten with tail are teachable.     (1)

From Axioms 4 If a kitten has green eyes, then it is not teachable .

It means if kitten is teachable then it does not have green eyes.  (2)

Thus from 1 and 2 we can say that:

If a kitten has a tail, then it does not have green eyes.

Statement 7.10 If a kitten has green eyes, then it does not love fish.

From Axioms 4 If a kitten has green eyes, then it is not teachable .

From Axiom 1 If a kitten loves fish, then it is teachable

From Axioms 1 and 4 If a kitten has green eyes, then it does not love fish.

options a,b,c are the right answer.

step-by-step explanation:

a linear parent function is always represented as y = x

if we write this function in the form of y=mx+c

⇒

or  

now if we plot a graph we will find these characteristics:

1) y intercept of the graph is zero so its a straight line passing through origin.

2) as we can see in both the forms of function written, values of x and y may be either positive or negative for the positive slope means points on the graph are either in first quadrant or in third one.

3) it's slope is one.