Which of these collections of subsets are partitions of abcd

Which of these collections of subsets are partitions of {a,b,c,d}? If not, why?

(a) {{a,b,d},{c,d}}

(b) {{a},{b,d},{c}}

Which of these collections of subsets are partitions of {a,b,c,d}? If not, why? (a) {{a,b,d},{c,d}} (b) {{a},{b,d},{c}} (c) {{a,b,d},{c,d},{ psi}}

a) {{a,b,d},{c,d}}

Union of {a,b,d} U {c,d} = {a,b,c,d} = Original set
So, union condition holds

Intersection of {a,b,d} and {c,d} = {d} = Non-empty
Since the intersection is NOT empty,

So, \'a\' is NOT a partition

b) {{a},{b,d},{c}}

Union {a} U {b,d} U {c} = {a,b,c,d} = Original set
So, union holds

{a} intersection {b,d} = NULL
{a} intersection {c} = NULL
{b,d} intersection {c} = NULL
So, intersection also holds

None of the subsets is a NULLSET

So, yes, B is a partition

c) {{a,b,d},{c,d},{NULL}}

We have a {NULL}

So, automatically, c is NOT a partition