06 excel4
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This document discusses nested functions and DeMorgan's Laws. It provides examples of using nested IF functions to evaluate complex formulas that depend on the results of inner expressions. DeMorgan's Laws state that NOT(AND(X,Y)) is equivalent to OR(NOT(X),NOT(Y)) and that NOT(OR(X,Y)) is equivalent to AND(NOT(X),NOT(Y)), which can be verified using truth tables. An example shows how to model college admissions decisions using nested IF statements to check multiple criteria.
06 excel4
- 1. Nested Functions How do we evaluate a complex formula? What are DeMorgan’s Laws? CS 105 Spring 2011 #1
- 2. Grade Example • Suppose there is 2% extra credit (column AK) • Solution 1: create column AN for “Points + EC” Y Y =IF(AK2=“Y”,AI2*102%,AI2) Then use • Solution 2: =VLOOKUP(AN2,AL2:AM12,TRUE) Y =VLOOKUP( IF(AK2=“Y”,AI2*102%,AI2) ,AL2:AM12,TRUE) CS 105 Spring 2011 #2
- 3. Nested Functions • In order to evaluate a complex formula like =VLOOKUP(IF(AK2=“Y”,AI2*102%,AI2),AL2:AM12,TRUE) 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”) 3 2 1 CS 105 Spring 2011 #3
- 4. DeMorgan’s Laws • 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: 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 CS 105 Spring 2011 #4
- 5. Example: College Admissions • A college grants admissions based on three criteria: SAT score (S), Letter score (L), and References (R) S L R Decision 1300 AND 8.5 AND 8.25 Strong accept 1200 AND 8.0 AND 7.80 Accept 1200 OR 7.5 OR 7.00 Reject … Manual … ELSE • Which of these formulas is correct? 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"))) CS 105 Spring 2011 #5
- 6. Testing Your Knowledge • How do we evaluate a complex formula? • What are DeMorgan’s Laws? CS 105 Spring 2011 #6