Pls help me with this questions:
9. Obtain the conjunctive normal form of the following propositions:
(a) \(\displaystyle P\, \land\, \left(P\, \rightarrow\, Q\right)\)
(b) \(\displaystyle Q\, \lor\, \left(P\, \land\, R\right)\, \land\, \urcorner \left( \left( P\, \lor\, R \right) \, \land \, Q\right)\)
10. Show that \(\displaystyle \left(P\, \rightarrow\, Q\right)\, \land\, \left(R\, \rightarrow\, Q\right)\, \leftrightarrow\, \left(P\, \lor\, R\right)\, \rightarrow\, Q\)
11. Let \(\displaystyle A\, =\, \left\{1,\, 2,\, 3,\, 4,\, 5,\, 6\right\}.\) Define \(\displaystyle R\) to be \(\displaystyle R\, \left\{x,\, y\, |\, x\, \leq\, y\right\}.\) Test whether \(\displaystyle R\) is Reflexive, Transitive, or Symmetric.
12. Let \(\displaystyle I\) be the set of integers. Prove that the algebra \(\displaystyle \left(I,\, +\right)\) is an abelian group.
This is for my brother.....maths is not my main.......having hard time explaining his doubts......!!! any help wud be grt...!!! i know this kind of posts are no gud...sorry....!!! btw this is from a question bank.....!!!!
9. Obtain the conjunctive normal form of the following propositions:
(a) \(\displaystyle P\, \land\, \left(P\, \rightarrow\, Q\right)\)
(b) \(\displaystyle Q\, \lor\, \left(P\, \land\, R\right)\, \land\, \urcorner \left( \left( P\, \lor\, R \right) \, \land \, Q\right)\)
10. Show that \(\displaystyle \left(P\, \rightarrow\, Q\right)\, \land\, \left(R\, \rightarrow\, Q\right)\, \leftrightarrow\, \left(P\, \lor\, R\right)\, \rightarrow\, Q\)
11. Let \(\displaystyle A\, =\, \left\{1,\, 2,\, 3,\, 4,\, 5,\, 6\right\}.\) Define \(\displaystyle R\) to be \(\displaystyle R\, \left\{x,\, y\, |\, x\, \leq\, y\right\}.\) Test whether \(\displaystyle R\) is Reflexive, Transitive, or Symmetric.
12. Let \(\displaystyle I\) be the set of integers. Prove that the algebra \(\displaystyle \left(I,\, +\right)\) is an abelian group.
This is for my brother.....maths is not my main.......having hard time explaining his doubts......!!! any help wud be grt...!!! i know this kind of posts are no gud...sorry....!!! btw this is from a question bank.....!!!!
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