# Misc 4 - Chapter 1 Class 11 Sets (Term 1)

Last updated at Jan. 27, 2020 by Teachoo

Miscellaneous

Misc 1

Misc 2 (i)

Misc 2 (ii) Important

Misc 2 (iii) Important

Misc 2 (iv)

Misc 2 (v)

Misc 2 (vi) Important

Misc 3

Misc 4 Important You are here

Misc 5

Misc 6

Misc 7 Important

Misc 8 Important

Misc 9 Important

Misc 10

Misc 11

Misc 12 Important

Misc 13 Important

Misc 14

Misc 15 Important

Misc 16 Important

Last updated at Jan. 27, 2020 by Teachoo

Misc 4 Show that the following four conditions are equivalent: (i) A ⊂ B (ii) A – B = Φ (iii) A ∪ B = B (iv) A ∩ B = A Showing Condition (i) is equivalent to Condition (ii). Let A ⊂ B This means all elements of A are in B, So, A has no element different from B ⇒ A – B = Φ Showing Condition (ii) is equivalent to Condition (iii). A – B = ∅ This means A has no elements different from B So, all elements of A are in B So, A ∪ B = B ⊂ - is a subset A ⊂ B if all elements of A are in B (i) A ⊂ B (ii) A – B = Φ (iii) A ∪ B = B (iv) A ∩ B = A Showing Condition (iii) is equivalent to Condition (iv). A ∪ B = B This means all elements of A are in B, So , the common elements of A and B must be the elements of A So, A ∩ B = A Thus, (i) ⇔ (ii) ⇔ (iii) ⇔ (iv) Thus, all the four conditions are equivalent.