Combining AND, OR and NOT with brackets

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Date:

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Quick Questions

Shade in the A or B circle for each question.

1. Without brackets, in what order is NOT A OR B AND C worked out?

A NOT first, then AND, then OR

B OR first, then AND, then NOT

2. Which condition means the same as A OR B AND C?

A (A OR B) AND C

B A OR (B AND C)

3. A = TRUE, B = FALSE, C = FALSE. What is (A OR B) AND C?

A TRUE

B FALSE

4. A = TRUE, B = FALSE, C = FALSE. What is A OR B AND C with no brackets?

A TRUE

B FALSE

5. A = TRUE, B = FALSE. What is NOT (A AND B)?

A TRUE

B FALSE

Match the Pairs

Draw a line connecting each item on the left to its match on the right.

Left column		Right column
1A OR B AND C		ANOT A AND B
2(A OR B) AND C		BMeans A OR (B AND C), because AND is worked out before OR when there are no brackets
3Brackets make NOT apply to a whole condition, so it is true only when both A and B are false		CA OR B is worked out first, then the result must be true together with C
4Without brackets, NOT is done first and only reverses the value right after it		DThe condition was worked out left to right. AND comes first: FALSE AND FALSE is FALSE, then TRUE OR FALSE is TRUE.
5IF Age < 12 OR Age > 65 AND HasTicket		ENOT (A OR B)
6TRUE OR FALSE AND FALSE = FALSE		FAND is done before OR, so HasTicket only applies to Age > 65. Brackets are needed: (Age < 12 OR Age > 65) AND HasTicket.

Definitions

(A OR B) AND C

Fill in the Blanks

Complete each line of code by filling in the missing parts.

IF (Age < 12 __ Age > 65) AND Paid THEN OUTPUT "Half price" ENDIF

IF ___ (Raining OR Windy) THEN OUTPUT "Play outside" ENDIF

Result <- (TRUE OR FALSE) ___ FALSE // Result is FALSE

Result <- TRUE __ FALSE AND FALSE // AND first, so Result is TRUE

Result <- NOT (TRUE AND _____) // Result is TRUE

Spot the Error

Shade in the letter of the line that contains an error.

Question 1

A IF (A OR B AND C THEN

B OUTPUT "Go"

C ENDIF

Question 2

A INPUT Age

B IF Age < 5 AND Age > 64 THEN

C OUTPUT "Child or senior"

D ENDIF

Question 3

A Rain <- FALSE

B Wind <- TRUE

C IF NOT Rain OR Wind THEN

D OUTPUT "Play outside"

E ENDIF

Question 4

A A <- TRUE

B R <- (A OR FALSE) AND FALSE

C OUTPUT R

D // Output is TRUE

Question 5

A INPUT Age

B INPUT Late

C IF Age < 18 OR NOT Late THEN

D OUTPUT "Young and on time"

E ENDIF

Answer Key

Combining AND, OR and NOT with brackets

Section A: Quick Questions

A — NOT first, then AND, then OR

B — A OR (B AND C)

B — FALSE

A — TRUE

Section B: Match the Pairs

A OR B AND C → Means A OR (B AND C), because AND is worked out before OR when there are no brackets

(A OR B) AND C → A OR B is worked out first, then the result must be true together with C

Brackets make NOT apply to a whole condition, so it is true only when both A and B are false → NOT (A OR B)

Without brackets, NOT is done first and only reverses the value right after it → NOT A AND B

IF Age < 12 OR Age > 65 AND HasTicket → AND is done before OR, so HasTicket only applies to Age > 65. Brackets are needed: (Age < 12 OR Age > 65) AND HasTicket.

TRUE OR FALSE AND FALSE = FALSE → The condition was worked out left to right. AND comes first: FALSE AND FALSE is FALSE, then TRUE OR FALSE is TRUE.

Section C: Definitions

(A OR B) AND C — Brackets are worked out first. Without them NOT is done first, then AND, then OR. So A OR B AND C means A OR (B AND C), and brackets change that order.

Section D: Fill in the Blanks

IF (Age < 12 OR Age > 65) AND Paid THEN
  OUTPUT "Half price"
ENDIF

IF NOT (Raining OR Windy) THEN
  OUTPUT "Play outside"
ENDIF

Result <- (TRUE OR FALSE) AND FALSE
// Result is FALSE

Result <- TRUE OR FALSE AND FALSE
// AND first, so Result is TRUE

Result <- NOT (TRUE AND FALSE)
// Result is TRUE

Section E: Spot the Error

A — The opening bracket has no closing bracket. Brackets must come in pairs. It should be IF (A OR B) AND C THEN so that A OR B is worked out first.

B — No age can be both under 5 and over 64, so AND is never true and nothing would be output. To match a child or a senior it must be OR: IF Age < 5 OR Age > 64 THEN.

C — Without brackets NOT is done first and only applies to Rain, so it is (NOT Rain) OR Wind. That is TRUE when it is windy. The brackets are needed so NOT applies to the whole of Rain OR Wind: IF NOT (Rain OR Wind) THEN.

B — These brackets make OR happen first: TRUE AND FALSE gives FALSE, not the TRUE the comment expects. AND is worked out before OR, so the brackets belong round FALSE AND FALSE: R <- A OR (FALSE AND FALSE).

C — The message says the person is young AND on time, so both parts must be true. OR would let in anyone under 18 even if they are late. It should be IF Age < 18 AND NOT Late THEN.