Equality of sets — recognize empty-set equivalence (Recovery-First on notation): In which case are A and B equal as sets?

Introduction / Context:Two sets are equal if they have precisely the same elements. The empty set Φ and {} are two notations for the same set with no elements. We verify each option’s membership.

Given Data / Assumptions:

• Φ and {} both denote the empty set
• W denotes whole numbers {0,1,2,…}

Concept / Approach:Compare members: if both collections contain exactly the same elements, they are equal; otherwise not. For empty sets, absence of elements matches perfectly.

Step-by-Step Solution:Option (b): Φ and {} → equal (both empty)Option (a): distinct lists (no equality)Option (c): {x ∈ W : x < 1} = {0} ≠ ΦOption (d): {Saturday, Sunday} ≠ {Sunday}Option (e): {} ≠ {0}

Verification / Alternative check:Cardinality check helps: |Φ| = 0, |{}| = 0, hence equal; options (c) and (d) clearly have different cardinalities.

Why Other Options Are Wrong:They either list different elements or different counts.

Common Pitfalls:Confusing {} with {0}; the latter contains the number zero and is not empty.

Final Answer:A = Φ, B = {}