) Prove that the set An := {T € Sn | sign(r) = 1} has n! elements for all n > 2. Show this by constructing a suitable bijective mapping between An and Sn \ An . Remark: Without justification, you may use the fact that if there is a bijective mapping between two (finite) sets, then these must have the same number of elements.

Q: Define a bijective map g : x2/3--->R.

A: Sol

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A: A lattice is a poset in which any two elements have a meet and a join. Draw the Hasse diagram.

Q: Lex 172,3,4). Consider the relation R on X defined as follows. R = ((1.1), 13), (2,2), (2.4), (3,1),…

A: I have solved both subpart using basic definition of equivalence relation and equivalence class.

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A: Given:

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Q: whether it is transitive. a) {(2, 2), (2, 3), (2, 4), (3, 2), (3, 3), (3, 4)} b) {(1, 1), (1, 2),…

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Q: State whether the statement is true or false : '' All relations are mapping but the converse is not…

A: we know that  All mapping are relation, but the converse is not true .