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Read the statement.


Doubling the dimensions of a rectangle increases the area by a factor of 4.


If p represents doubling the dimensions of a rectangle and q represents the area increasing by a factor of 4, which are true? Check all that apply.



Ap → q represents the original conditional statement.

B~p → ~q represents the inverse of the original conditional statement.

Cq → p represents the original conditional statement.

D~q → ~p represents the converse of the original conditional statement. p → ~q represents the contrapositive of the original conditional statement

Verified Answer :

timichaeljordan
Ap → q represents the original conditional statement. 
JeanaShupp

Answer: Option (A) is true "p → q represents the original conditional statement".


Step-by-step explanation:

Let's check all the options

A. Let l × b be the dimensions of the rectangle such that Area of rectangle=l × b

If you doubles the dimensions then Area of new rectangle =2l × 2b =4(l × b)=4 times the area of rectangle.

∴If dimensions increased by double then area increases by factor of 4.

⇒p → q represents the original conditional statement.

B. This option says if dimensions of rectangle do not increased by double then the area do not increased by factor of 4.....>which is not true .

For example if we increased only the length of the rectangle by factor 4 then the Area of the new rectangle=4l×b=4(l+b) which is the area of the original rectangle.

∴ B is not true.

C. This option is false as we already got the original statement in option A.

D. This says that if There is no increase in area of rectangle by 4 then its dimension do not increased.....>which is the converse of the inverse statement (which we already proved wrong in B)of the original statement.

∴ Option D is also not true.

So only option A is the correct option.

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