Operations On Sets

Step 1: Use the formula for cardinality of union of two sets:
Step 2: Given:
Step 3: The intersection can have: (since the smaller set has 3 elements)
Step 4: Find minimum value of :
Step 5: Find maximum value of :
Step 6: Hence,

Step 1: Find set by solving the quadratic equation:
Step 2: Find the intersection of sets and :
Step 3: Form the Cartesian product:

Step 1: Find some elements of set . For : For : For : Thus,
Step 2: Find some elements of set . For : For : For : Thus,
Step 3: Compare the sets.
but
but
Step 4: Since neither set is a subset of the other and they are not equal, the correct conclusion cannot be determined as (A), (B), or (C).