Steve said that [5, 12) is the interval notation that represents the set of all rea
numbers greater than or equal to 5 and less than 12. joe says that (5, 12] is
correct interval notation. who is correct and justify why?

I am not sure which symbol you meant to include so will do all four of them:

y > -5   >     (-5, ∞)

y ≥ -5   >     [-5, ∞)

y < -5   >     (-∞, -5)

y ≤ -5   >     (-∞, -5]

The PARENTHESIS is used when the number is NOT included (open dot).

The BRACKET is used when the number IS included (closed dot).