In each of the following, determine whether the statement is true or false. If it is
true, prove it. If it is false, give an example.
(i) If x ∈ A and A ∈ B , then x ∈ B
(ii) If A ⊂ B and B ∈ C , then A ∈ C
(iii) If A ⊂ B and B ⊂ C , then A ⊂ C
(iv) If A ⊄ B and B ⊄ C , then A ⊄ C
(v) If x ∈ A and A ⊄ B , then x ∈ B
(vi) If A ⊂ B and x ∉ B , then x ∉ A
Decide, among the following sets, which sets are subsets of one and another:
A = { x : x ∈ R and x satisfy x
2
– 8x + 12 = 0 },
B = { 2, 4, 6 }, C = { 2, 4, 6, 8, . . . }, D = { 6 }
Show that the set of letters needed to spell “ CATARACT ” and the
set of letters needed to spell “ TRACT” are equal.
(v)
Which one of the following disciplines attempts temporal synthesis?
(a) Sociology
(c) Anthropology
(b) Geography
(d) History
Which one of the following questions is related to cause-effect relationship?
(a) Why
(c) What
(b) Where
(d) When
Which one of the following features can be termed as ‘physical feature’?
(a) Port
(c) Plain
(b) Road
(d) Water park
Which one of the following scholars coined the term ‘Geography’?
(a) Herodotus
(c) Galileo
(b) Erathosthenese
(d) Aristotle
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