# 1

Nested FunctionsNested Functions

How do we evaluate a complex formula?

What are DeMorgan’s Laws?

CS 105 Spring 2011

# 2

Grade Example

• Suppose there is 2% extra credit (column AK)

• Solution 1: create column AN for “Points + EC”

Then use• Solution 2:

CS 105 Spring 2011

Y

Y

Y=IF(AK2=“Y”,AI2*102%,AI2)

=VLOOKUP(AN2,AL2:AM12,TRUE)

=VLOOKUP( ,AL2:AM12,TRUE)IF(AK2=“Y”,AI2*102%,AI2)

# 3

• In order to evaluate a complex formula like

start by evaluating the inner parts

• The overall formula can be evaluated once the values of the inner sub-expressions are known

• A more complex example:

IF(ISERROR(VLOOKUP(value,range,col)),”No”,”Yes”)

CS 105 Spring 2011

Nested Functions

=VLOOKUP(IF(AK2=“Y”,AI2*102%,AI2),AL2:AM12,TRUE)

123

# 4

• Consider the following formulas:a) NOT(AND(X, Y))b) AND(NOT(X), NOT(Y))c) NOT(OR(X, Y))d) OR(NOT(X), NOT(Y))

• The formulas (a) and (d) are equivalent, and so are formulas (b) and (c)

• We can verify this with truth tables:

CS 105 Spring 2011

DeMorgan’s Laws

X Y AND(X,Y) NOT(AND(X,Y))

NOT(X) NOT(Y)

OR(NOT(X), NOT(Y))

0 0 0 1 1 1 1

0 1 0 1 1 0 1

1 0 0 1 0 1 1

1 1 1 0 0 0 0

# 5CS 105 Spring 2011

Example: College AdmissionsExample: College Admissions• A college grants admissions based on three

criteria: SAT score (S), Letter score (L), and References (R)

• Which of these formulas is correct?

S L R Decision

1300 8.5 8.25 Strong accept

1200 8.0 7.80 Accept

1200 7.5 7.00 Reject

… ELSE … Manual

AND AND

AND AND

OR OR

IF(AND(S>=1300,L>=8.5,R>=8.25), "Strong accept",

IF(AND(S>=1200, L>=8, R>=7.8), "Accept",

IF(OR(S<1200, L<7.5, R<7), "Reject", "Manual")))

IF(OR(S<1200,L<7.5,R<7), "Reject",

IF(OR(L<8,R<7.8),"Manual",

IF(OR(S<1300,L<8.5,R<8.25),"Accept",

"Strong accept")))

# 6

• How do we evaluate a complex formula?

• What are DeMorgan’s Laws?

CS 105 Spring 2011

Testing Your Knowledge