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1) Let be a function from Z to R, such that , then is
a) an increasing function
b) a strictly increasing function
c) a decreasing function
d) an onto function
Consider the following assertions about the sets A, B and C. Write them down in the language of predicate logic. Use only the constructions of predicate logic (∀, ∃, ¬, ⇒, ∧, ∨) and the element of symbol (∈). Do not use derived notions (∩, ∪, =, etc.).
Hint “A is a subset of B” can be formalized as ∀x. x ∈ A =⇒ x ∈ B.
(i)
(ii)
(iii) The sets A and B are equal.
Every element of A is in the set B or the set C.
If A is disjoint from B then B and C overlap.
Let S={2, 4, 7}
and T={1, 3, 5}
. Find f(S×T)
if
- f(x,y)=14x/3y
In a high school, 50 students are surveyed and asked about the interest of the student. 23 students interested in English subject, 14 interested in Mathematics, and 11 in Urdu, 6 is in English an mathematics, 4 is in English and Urdu , and 5 is in English and Urdu. 15 students not interested in any subject. How many students interested in 3 subjects? Also represent your answer by using Venn diagram.
The study involved 55 students (23 male, 32 female) and used a mixed methods approach, involving a questionnaire with open ended questions, Likert scale questionnaire and interviews that aimed to determine students' perceptions of their performance. Five main areas were investigated with the open-ended questions: defining clinical reasoning; advantages and disadvantages of clinical case studies; the effectiveness of clinical case studies in comparison to real patients; and whether clinical case studies helped students working in a sports injury clinic. Students completed a 5-point Likert scale that asked three statements regarding the clinical environment. Following the questionnaire, a sample of 15 students were randomly selected for individual interviews. The results suggested that the students' responses were generally in favour of the use of clinical case studies to aid the development of confidence, communication and clinical reasoning.
1) Identify the premises of above argument
1. Suppose that f is defined recursively by:
f (0) 5= and f n( + =1) 2fn+5. Find f(1), f(2), f(3) and f(4)?
In the following argument, determine the validity or otherwise of the
Statement:
a) “If you aren’t polite, you won’t be treated with respect. You aren’t
treated with respect. Therefore, you aren’t polite.
b) “If you play football during a thunderstorm, you’ll get hit by lightning.
You didn’t get hit by lightning. Therefore, you didn’t play football in a
thunderstorm”
Therefore, taxes are lowered.”
(i) Write out the propositional statements in the above argument?
(ii) State the premise(s) and conclusion in the argument?
(iii) Using a truth table, determine the validity of the argument?
Let f be a function from Z to R, such that f(x)=x/10, then f is
a) an increasing function
b) a strictly increasing function
c) a decreasing function
d) an onto function
Find f∘g and g∘f , where f(x)=x^2+2x+1 and g(x)=x^2-20, are functions from R to R.
Type/Insert your answer here!
i) Let S={2,4,7} and T={1,3,5}. Find f(S×T) if
f(x,y)=⌊14x/3y⌋
Type/Insert your answer here!
Note: No partial credit would be admissible in this question
f(x,y)=x^2+y^3
Type/Insert your answer here!
Note: No partial credit would be admissible in this question
