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Order the expressions by choosing or

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order the expressions by choosing or
A: –

Concept:

Use a truth-based partial order.
For Boolean expressions E and F, define E ≤ F if every assignment that makes E true also makes F true (i.e., the truth set of E is a subset of the truth set of F).
In this order, adding OR tends to increase the truth set, so expressions with OR are often greater or equal.
– One clear example: Let E1 = p and E2 = p or q.

Truth sets: T(E1) = {assignments with p = true}, T(E2) = {assignments with p = true or q = true}.
Since T(E1) ⊆ T(E2), E1 ≤ E2. There are assignments (p = false, q = true) where E2 is true but E1 is not, so E2 ≰ E
1. Therefore: p ≤ p or q.
– If you provide the specific expressions, I’ll order them accordingly using this rule.

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