- Last part of section 2.3
- Examples / problems
- Write predicates that are true if and only if…
- Predicate = boolean-valued function
- e.g., p(x) = x is a dog
- x is between 1 and 7 (inclusive)
- p(x) = x ≥ 1 ∧ x ≤ 7
- p(x) = 1 ≤ x ≤ 7
- x is greater than y
- p(x,y) = x > y
- Predicates can be multivariable, just like other functions
- p(9,-3) = true
- p(9,12) = false
- s is a subset of r and contains the number 3
- p(s,r) = s ⊆ r ∧ 3 ∈ s
- Give example(s) of values for which this predicate is true, and example(s)
for which it is false
- True: p( { …, -1, 1, 3, … }, ℝ )
- False: p( {1,2}, {3,4} )
- Predicate = boolean-valued function
- Write specifications for…
- The set of negative solutions to the inequality x sinx > 3
- Visually this set will be increasingly large subintervals of the negative
reals, as x gets sufficiently negative to multiply by a sine value near -1
and produce a product greater than 3
- { x ∈ ℝ | x sinx > 3 ∧ x < 0 } (1st form of set builder notation)
- Visually this set will be increasingly large subintervals of the negative
reals, as x gets sufficiently negative to multiply by a sine value near -1
and produce a product greater than 3
- The set of odd numbers
- Ideas: s ∈ ℤ, s = 2n+1, n ∈ ℤ
- Putting ideas together: { 2n + 1 | n ∈ ℤ } (2nd form of set builder notation)
- The set of negative solutions to the inequality x sinx > 3
- Write predicates that are true if and only if…
- Quantifiers
- Read section 2.4