Ch 1.3.4: Logic | Translating from English into Logical Expressions
In this Lecture i discussed Translating from English into Logical Expressions
0:09 EXAMPLE 16 Express the statement “Every student in this class has studied calculus” using predicates and quantifiers.
3:35 EXAMPLE 17 Use predicates and quantifiers to express the system specifications “Every mail message larger than one megabyte will be compressed” and “If a user is active, at least one network link will be available.”
6:26 EXAMPLE 18 Consider these statements. The first two are called premises and the third is called the conclusion.The entire set is called an argument.
“All lions are fierce.”
“Some lions do not drink coffee.”
“Some fierce creatures do not drink coffee.”
Let P (x): “x is a lion,” Q(x): “x is fierce,” and R(x): “x drinks coffee,” be the statements.
Assuming that the domain consists of all creatures, express the statements in the argument using quantifiers and P (x), Q(x), and R(x).
9:50 EXAMPLE 19 Consider these statements, of which the first three are premises and the fourth is a valid conclusion.
“All hummingbirds are richly colored.”
“No large birds live on honey.”
“Birds that do not live on honey are dull in color.”
“Hummingbirds are small.”
Let P (x), Q(x), R(x), and S(x) be the statements “x is a hummingbird,” “x is large,” “x lives on honey,” and “x is richly colored,” respectively.
Assuming that the domain consists of all birds,express the statements in the argument using quantifiers and P (x), Q(x), R(x), and S(x).
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