Test-Ideas Catalog: Test Ideas for Mixtures of ANDs and ORs

This catalog applies to expressions that combine ANDs and ORs. As a reminder, here’s how to derive test requirements for homogenous expressions:

A1 && A2 && … && An:

one test idea with All Ai’s true
N cases, each of which has exactly one term false.

Example:


A && B && C
A	B	C
true	true	true
FALSE	true	true
true	FALSE	true
true	true	FALSE

A1 || A2 || … || An:

one test idea with All Ai’s false
N cases, each of which has exactly one term true.

Example:


**A		B
A	B	C
FALSE	FALSE	FALSE
FALSE	true	FALSE
true	FALSE	FALSE
FALSE	FALSE	true

Two Boolean Operators


**(A && B)		C**
A	B	C
FALSE	true	true
true	true	FALSE
FALSE	true	FALSE
true	FALSE	FALSE


**A && (B		C)**
A	B	C
true	FALSE	FALSE
true	FALSE	true
true	true	FALSE
FALSE	FALSE	true


**A		(B && C)**
A	B	C
true	true	FALSE
FALSE	true	true
FALSE	FALSE	true
FALSE	true	FALSE


**(A		B) && C**
A	B	C
FALSE	FALSE	true
FALSE	true	true
true	FALSE	true
FALSE	true	FALSE

Three Boolean Operators One And

To help find an expression, read down the columns. The ANDs drift from the left to the right as you read.


**(A && B)		C		D**
A	B	C	D		A	B	C	D
FALSE	true	true	FALSE		FALSE	FALSE	true	FALSE
true	true	FALSE	FALSE		FALSE	true	true	FALSE
FALSE	true	FALSE	FALSE		true	FALSE	true	FALSE
true	FALSE	FALSE	FALSE		FALSE	FALSE	true	true
true	FALSE	FALSE	true		FALSE	true	FALSE	FALSE


**A && (B		C		D)**
A	B	C	D		A	B	C	D
true	FALSE	FALSE	FALSE		FALSE	true	FALSE	FALSE
true	FALSE	true	FALSE		FALSE	true	FALSE	true
true	true	FALSE	FALSE		FALSE	true	true	FALSE
true	FALSE	FALSE	true		true	true	FALSE	FALSE
FALSE	FALSE	FALSE	true		FALSE	FALSE	FALSE	true


**A		(B && C)		D**
A	B	C	D		A	B	C	D
true	true	FALSE	FALSE		FALSE	true	true	FALSE
FALSE	true	true	FALSE		FALSE	FALSE	FALSE	true
FALSE	FALSE	true	FALSE		true	FALSE	true	FALSE
FALSE	true	FALSE	FALSE		FALSE	FALSE	true	true
FALSE	true	FALSE	true		FALSE	FALSE	true	FALSE


**(A		B) && (C		D)**
A	B	C	D		A	B	C	D
FALSE	FALSE	FALSE	true		FALSE	FALSE	FALSE	true
FALSE	true	FALSE	true		FALSE	true	FALSE	true
true	FALSE	true	FALSE		true	FALSE	FALSE	true
FALSE	true	FALSE	FALSE		FALSE	FALSE	true	true
					FALSE	FALSE	true	FALSE

Three Boolean Operators Two Ands

To help find an expression, read down the columns. The ORs drift from the right to the left as you read


**(A && B && C)		D**					**((A && B)
A	B	C	D		A	B	C	D
true	true	true	FALSE		FALSE	true	true	true
FALSE	true	true	FALSE		true	true	FALSE	true
true	FALSE	true	FALSE		FALSE	true	FALSE	true
true	FALSE	true	true		true	FALSE	FALSE	true
true	true	FALSE	FALSE		true	FALSE	true	FALSE


**A && B && (C		D)**					**A && (B
A	B	C	D		A	B	C	D
true	true	FALSE	true		true	true	true	FALSE
FALSE	true	FALSE	true		true	FALSE	true	true
true	FALSE	FALSE	true		true	FALSE	FALSE	true
true	true	FALSE	FALSE		true	FALSE	true	FALSE
true	true	true	FALSE		FALSE	FALSE	true	true


**A && (B		C) && D**					**(A
A	B	C	D		A	B	C	D
true	FALSE	FALSE	true		FALSE	FALSE	true	true
true	FALSE	true	true		FALSE	true	true	true
true	true	FALSE	true		true	FALSE	true	true
FALSE	FALSE	true	true		FALSE	true	FALSE	true
true	FALSE	true	FALSE		FALSE	true	true	FALSE


**(A && B)		(C && D)**					**A
A	B	C	D		A	B	C	D
FALSE	true	true	true		FALSE	true	true	true
true	true	true	FALSE		FALSE	FALSE	true	true
FALSE	true	FALSE	true		FALSE	true	FALSE	true
true	FALSE	true	FALSE		true	true	true	FALSE
					FALSE	true	true	FALSE