Consider the first statement:

x+y>−2

Take x =1 and y=0 . we get (1+0)>-2 .

Here x>0 is satisfied.

Take x =-1 and y=0.we get (-1+0)>-2.

Here x>0 not satisfied.

Second statement

x−y<−2

Take x=1 and y=4 . we get (1-4)<-2.

here x>0 is satisfied.

Take x =-1 and y=2 .we get (-1-2)<-2.

here x>0 is not satisfied.

Taking both the statements together. we get

x+y>−2

x−y<−2

Lets make the inequality symbols same for both of the equations:

x+y>-2

-x+y>2 --->Multiplying by -1 therefore getting the inequality similar to that of the first one. (Inequality symbol gets changed)

Note: In inequality the only operation can be performed when two inequalities are there is addition.

Therefore we get 2y>0 ----> y>0

we can substitute the value of y that is greater than 0 we still cannot determine if x>0.

Therefore in my opinion the answer is E.
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