Question

an equals method is supposed to provide an equivalence relation among the objects of a class, this means that if a, b, and care non-null objects of the class then i. a equals(s) is true ii. a.equals(b) has the same value as b. equals (a) ii. if a. equals (b) is true and b. equals() is true, then a, equals (c) is true State whether the following definitions of equals are valid. If they are not explain why. A.) Two circles are equal if they have the same area B.) Two circles are equal if their radii are within 10% of each outher. C.) Two integers are equal if they have the same remainder when divided by a specific integer-for example, when divided by 3. D.) Two integers are equal if the second integer is a multiple of the first ws

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Answer 1

A.

Yes two circles can be equal when they have same area.

as if

Area1 = Area2 => pi* r1*r1= pi*r2*r2

=> r1^2=r2^2

as r1 and r2 can't be negative

=>r1=r2

So circles have equal radii also.

B.

No two circles are not equal when their radii is within10% of each other.

For example circle with radii 100 and 105 are not equal even the ave radii within 10%.

C.

No two integers are not equal when they give same remainder when divided by given integers.

For example, 5,8,11.

These three give remainder 2 when divided by 3. Though they are not equal.

D.

No thats not the case.

4,,6,8 are multiples of 2 but they are not equal.