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Practice bank for UCAT Decision Making questions testing your ability to identify logically equivalent statements and correct negations.
Two statements are logically equivalent if they are true and false in exactly the same situations.
| Original | Equivalent Form |
|---|---|
| If P then Q | If not Q then not P (contrapositive) |
| All A are B | If something is A, then it is B |
| No A are B | If something is A, then it is not B |
| Not (P and Q) | (Not P) or (Not Q) — De Morgan's Law |
| Not (P or Q) | (Not P) and (Not Q) — De Morgan's Law |
| Original | NOT Equivalent |
|---|---|
| If P then Q | If Q then P (converse) |
| If P then Q | If not P then not Q (inverse) |
| Some A are B | All A are B |
The negation of a statement is the statement that is true in exactly the opposite situations.
| Statement | Negation |
|---|---|
| All A are B | Some A are not B |
| No A are B | Some A are B |
| Some A are B | No A are B |
| Some A are not B | All A are B |
| P and Q | Not P or not Q |
| P or Q | Not P and not Q |
| If P then Q | P and not Q |
This is a critical one: the negation is NOT "If not P then not Q."
The negation of "If P then Q" is "P and not Q" — i.e., the condition holds but the result does not.
Complete the 10 assessment questions. Each presents a statement and asks for its equivalent or its negation.
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