DM - Lattice & Group -Q13

+1 vote

Let L be the set of all propositions generated by P and Q (Where P and Q are Two Propositions) using at most one of the following logical operations : \wedge, \vee, \oplus , \rightarrow, \leftrightarrow, \uparrow, \downarrow, Where \uparrow, \downarrow are NAND and NOR operators respectively.

i.e. L = \{P,Q, P\wedge Q,P \vee Q,P \oplus Q ,P \rightarrow Q,P \leftrightarrow Q,P \uparrow Q,P \downarrow Q\}

A Relation R is defined on L such that (a,b) \in R \,\,\,if\,\,and\,\,only\,\,if\,\, " a \rightarrow b"  is Tautology. 

Which of the following is False ?

(A). (L,R) is a poset.

(B). (L,R) is a poset but not a lattice.

(C). (L,R) is a lattice.

(D). None

asked Jun 27 in Discrete Maths by gbeditor (44,560 points)
reshown 4 days ago by gbeditor

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