Worksheets › Class 7 › Logic: If–Then, AND, OR, NOT › Cheat sheet
Class 7 Logic: If–Then, AND, OR, NOT: cheat sheet
CBSE Computational Thinking and AI. Logic decides whether statements are True or False. AND, OR and NOT combine them, and Venn diagrams count groups that overlap.
Key ideas
- A statement is either True or False; AND, OR and NOT build bigger statements from smaller ones.
- P AND Q is True only when both are True; P OR Q is True when at least one is True.
- NOT turns True into False and False into True; work out brackets first.
- An if–then rule is broken only by a case where the “if” part holds but the “then” part does not.
- In a Venn diagram, people in both groups sit in the overlap and must be counted once.
- A rule learned from labelled examples must fit all of them.
Remember
| AND | True only if both are True |
| OR | False only if both are False |
| NOT | NOT True = False; NOT False = True |
| At least one group | A + B − both |
| Neither | total − (A + B − both) |
| Example | 30 children, 18 like tea, 12 like milk, 5 both → 25 like one, 5 neither |
Watch out
- Reading OR as “only one”: in logic, P OR Q is also True when both are True.
- Applying NOT to only part of a bracket, or forgetting the brackets.
- Adding the two groups without taking away the overlap.
Worked example
(a) Rule: if it is a Saturday or a Sunday, the library opens at 10 a.m.; on other days it opens before 10 a.m. Thursday: opens at 10 a.m. Tuesday: opens at 8 a.m. Friday: opens at 9 a.m. Saturday: opens at 10 a.m. Sunday: opens at 10 a.m. Which day breaks the rule? (b) P is False and Q is True. Is "NOT P OR NOT Q" True or False?
Working: (a) Thursday is a weekday but opens at 10; (b) put P = False, Q = True and work out the brackets first
Answer: (a) Thursday; (b) True
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