First time here? Checkout the FAQ!
0 votes

Let f : AB and g : BC denote two functions. Consider the following two statements:
S1 : If both f and g are injections then the composition function : AC is an injection.
S2 : If the function : A → C is surjection and g is an injection then the function f is a surjection.
S3 : If h(a) = g(f(a)) and h(a) is onto then g must be onto, where ∀a, aA.
Which of the above statements are valid?

asked in Mathematical Logic by Boss (9.1k points) 4 64 210 | 69 views
all valid?
I couldnt find any contradicting example.
What is your approach to above problem?

How did you started?
Just took 3 sets with cardinalities 3/4 and try to have simple mappings. Just you need to check if you can contadict the statement. There is no specific rule . I hope you get it.
please explain 3rd statement

There is some function h: A->C which is onto. 

Given that h(a) = g( f(a) ), try to find a function 'g' which isnt onto. If you can find, then you have contradicted the statement.

1 Answer

+1 vote

Let f : A → B and g : B → 

S1: if f and g are injection fuction then composition function  gof :A → C is an injection. ----> this statement true its well known property.

S2:If the function gof : A → C is surjection and g is an injection then the function f is a surjection.

here keypoint is g is injection fuction.

means that  g(f(x) = g(y) -----> f(x) = y  so that fuction f is surjection

S3:If h(a) = g(f(a)) and h(a) is onto then g must be onto, where ∀aa ∈ A

all of the statement true. its all property .

answered by Boss (7.1k points) 5 40 149

No related questions found

Quick search syntax
tags tag:apple
author user:martin
title title:apple
content content:apple
exclude -tag:apple
force match +apple
views views:100
score score:10
answers answers:2
is accepted isaccepted:true
is closed isclosed:true
Top Users Oct 2017
  1. Arjun

    23462 Points

  2. Bikram

    17108 Points

  3. Habibkhan

    8560 Points

  4. srestha

    6314 Points

  5. Debashish Deka

    5458 Points

  6. jothee

    5038 Points

  7. Sachin Mittal 1

    4882 Points

  8. joshi_nitish

    4416 Points

  9. sushmita

    3996 Points

  10. Rishi yadav

    3868 Points

Recent Badges

Notable Question Sanjay Sharma
Notable Question Warrior
Notable Question sid1221
Nice Answer 2018
Good Question Arjun
Nice Question mitalitak
Great Question Arjun
Popular Question Tesla!
Nice Question makhdoom ghaya
Popular Question Sankaranarayanan P.N
27,348 questions
35,204 answers
33,328 users