Statements and Quantifiers Fill in the blanks to complete the following sentences. 1. The ______________ of a logical statement has the opposite truth value of the original statement. 2. _______________ are logical statements presented as the facts used to support…
Figure 2.14 Not all logical arguments are valid, and the ongoing fight for equal rights proves that much progress has yet to be made. (credit: “The Steam Roller” by Library of Congress Prints and Photographs Division, public domain) Learning Objectives After completing…
Figure 2.12 De Morgan’s Laws were key to the rise of logical mathematical expression and helped serve as a bridge for the invention of the computer. (credit: modification of work “Golden Gate Bridge (San Francisco Bay, California, USA)” by James St. John/Flickr,…
Figure 2.11 How your logical argument is stated affects the response, just like how you speak when holding a conversation can affect how your words are received. (credit: modification of work by Goelshivi/Flickr, Public Domain Mark 1.0) Learning Objectives After completing this…
Figure 2.10 If-then statements use logic to execute directions. (credit: “Coding” by Carlos Varela/Flickr, CC BY 2.0) Learning Objectives After completing this section, you should be able to: Computer languages use if-then or if-then-else statements as decision statements: For example, the following…
Figure 2.8 Just like solving a puzzle, a computer programmer must consider all potential solutions in order to account for each possible outcome. (credit: modification of work “Deadline Xmas 2010” by Allan Henderson/Flickr, CC BY 2.0) Learning Objectives After completing this section,…
Figure 2.6 A person seeking their driver’s license must pass two tests. A compound statement can be used to explain performance on both tests at once. (credit: modification of work “Drivers License -Teen driver” by State Farm/Flickr, CC BY 2.0) Learning Objectives…
Figure 2.2 Construction of a logical argument, like that of a house, requires you to begin with the right parts. (credit: modification of work “Barn Raising” by Robert Stinnett/Flickr, CC BY 2.0) Learning Objectives After completing this section, you should be able…
Figure 2.1 Logic is key to a well-reasoned argument, in both math and law. (credit: modification of work “Lady Justicia holding sword and scale bronze figurine with judge hammer on wooden table” by Jernej Furman/Flickr, CC BY 2.0) Chapter Outline 2.1 Statements and…
Subsets The number of subsets of a finite set AA is equal to 2 raised to the power of n(A)n(A), where n(A)n(A) is the number of elements in set AA: Number of Subsets of Set A=2n(A)A=2n(A). Set Operations with Two Sets The cardinality of AA union B:n(A∪B)=n(A)+n(B)−n(A∩B)