Any equation or inequality with variables in it is a predicate in the domain of real numbers. for the following statement, tell whether the statement is true or false. (∀x)(x4> x)

The statement is given by:

∀ x ,  

This statement is false

Since, if we consider,

then we have:

Also, we know that:

( Since, two number with same numerator; the number with greater denominator is smaller than the number with the smaller denominator )

Hence, we get:

when

Hence, the result :

is not true for all x belonging to real numbers.

Hence, the given statement is a FALSE statement.

answer: all of the odd numbers were opened

the first person was the one that was opening all of the lockers. since one is odd, this causes all of the odd number lockers to be opened in the end.