Questions on Conditional Logic

The Student

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Can the following statement be an if and only if statement? X + 5 = 7 if and only if X = 2. If so, is it also true to say that X + 5 = 7 if X = 2, which is just leaving out the "only if" part?
 
Can the following statement be an if and only if statement?

X + 5 = 7 if and only if X = 2. ............Yes

If so, is it also true to say that X + 5 = 7 if X = 2, ...............Yes


which is just leaving out the "only if" part?

Only if part claims that if x =2 then x+5 = 7
.
 
Note that dropping the "only if" part and writing "if x= 2 then x+ 5= 7" is NOT the same statement as the original "x+ 5= 7 if and only if x= 2" because it leave open the possibility that "x+ 5= 7" for some value of x other than 2.
 
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