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What are the two equivalent translations of an "unless" statement?¬p ∨ qp → q¬p ∨ ¬qp → qp ∨ qp → ¬qp ∨ q¬p → q

Question

What are the two equivalent translations of an "unless" statement?¬p ∨ qp → q¬p ∨ ¬qp → qp ∨ qp → ¬qp ∨ q¬p → q

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Solution

The two equivalent translations of an "unless" statement in logic are:

  1. ¬p ∨ q: This is read as "not p or q". It means that either the statement p is not true, or the statement q is true.

  2. p → q: This is read as "p implies q". It means that if p is true, then q must also be true.

These two statements are logically equivalent, meaning that they express the same truth conditions. In other words, they will both be true in exactly the same situations, and false in exactly the same situations.

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