# 03 - Association

1. Boolean algebra does have some of its own laws, it also simply borrows some from regular algebra. Association involves:

grouping variables into brackets

a trick of binary arithmetic that allows easy cancellation of factors

the fact that the order of the variables does not matter

the fact that multiplying all at once is the same as multiplying individually

2. The Associative Law is what allows you to group variables into brackets, and to break brackets apart again

FALSE

TRUE

3. In Boolean algebra, A+B+C could be laid out as (A+B)+C or as A+(B+C)

TRUE

FALSE

4. Consider the following and select the correct equivalent statement: (2+3)+4= 9

(2 + 3 + 4) * 2 = 9

2 * 3 * 4 = 9

5. The associative law states that if the parentheses (brackets) are rearranged in any way, the values of the expressions will also be immediately and always altered.

TRUE

FALSE

6. Associativity is not the same as commutativity, which addresses whether or not the order of two operands changes the result

FALSE

TRUE

7. Formally, a binary operation ? on a set S is called associative if it satisfies the associative law: (x ? y) ? z =

x ? (y ? z) for all x, y, z in S.

x + (y + z) for all x, y, z in S.

xyz for all x, y, z in S.

x (y z)+ x for all x, y, z in S.

8. Assuming a binary operation is associative, ((ab)c)d could also be written as:
```((ab)c)d
(ab)(cd)
(a(bc))d
a((bc)d)
a(b(cd))
abcd```

Option 2 and 3 are both valid

Option 1

All options are valid but the last option 'abcd' makes the most sense because the brackets, in all cases, are unnecessary

Option 1 and 6 are both valid

9. Consider the following example and fill in the blanks.
```The concatenation of the three strings
"hello",
" ",
"world"

can be computed by concatenating the first two strings
(giving "hello ")
and appending the third string ("world"),

or by joining the second and third string (giving "
world")
and concatenating the first string ("hello") with the
result. The two methods produce the same result;
string concatenation is _____________________```

commutative

concatenative

NOT associative

associative

10. (A + B) + C could also be written as:

A * (B + C)

A (B + C)

ABC

A + (B + C)

11. (A B) C could also be written as:

A + (BC)

A (B C)

A + B + C

A

12. Associative Law: (A + B) C = A (B C)

FALSE

TRUE

13. Associative law: (A + B) + C = A + (B + C)

FALSE

TRUE

14. The associative law also states that A + A B = A

FALSE

TRUE

15. The following is demonstrating which law?: A + (B + C) = (A + B) + C = A + B + C

the OR Associative Law

the NON Associative Law

the AND Associative Law

the three factor ASSOCIATION FACTORIAL LAW

16. Complete the equation for the AND Associative Law: A(B.C) = (A.B)C =

AB+C

C + A * B

A . B . C

A + B + C

17. The Absorptive law is identical to the Associative law >> A + (A.B) = A

FALSE

TRUE

18. The Associative law allows the_________________ from an expression and regrouping of the variables.

improving of solutions by changing sign (e.g. OR to AND or AND to OR)

removal of brackets

doubling up of brackets

simplification of any use of OR gates

19. The following is correctly depicting the OR Associative law: A + (B + C) = (A + B) + C = A + B + C

FALSE

TRUE

20. It is useful to remember that in Boolean Algebra the '+' in ordinary arithemetic is similar to the 'OR' and the '*' is similar to an 'AND'.

TRUE

FALSE