partition of set means:
(1) each partition must have some element means can't be empty.
(2) all partition can't have any common elements
(3) when we take union of all partition , whole set should be generate.
let's check option by option-
a.[{x:x>4},{x:x<5}] ,this fails 2nd condition so cant be partitions because partitions have common elements
b.[{x:x>0},{0},{x:x<0}],these partitions satisfied all three conditions because each partition have some element,all partition does not have any common elements and when we take union of all three partitions we will get real no. set.
c.[{x:x^2>11},{x:x^2<11}]-same reason as option a
