Mathematics, 03.10.2019 02:20 jaydostm9540
Prove that p (p) = (qa ~ q)] is a tautology.
Answers: 2
![P \leftrightarrow [(\lnot P) \rightarrow (Q \land \lnot Q)]](/tpl/images/0284/9635/39c43.png)
is a tautology.![P \leftrightarrow [(\lnot P) \rightarrow (Q \land \lnot Q)] \equiv](/tpl/images/0284/9635/bb069.png)
![\equiv (P \land [(\lnot P)\rightarrow (Q \land \lnot Q)]) \lor(\lnot P \land \lnot [(\lnot P)\rightarrow (Q \land \lnot Q)])](/tpl/images/0284/9635/db9f0.png)
by the logical equivalences involving bi-conditional statements![\equiv (P \land [\lnot(\lnot P)\lor (Q \land \lnot Q)]) \lor(\lnot P \land \lnot [\lnot(\lnot P)\lor (Q \land \lnot Q)])](/tpl/images/0284/9635/166c4.png)
by the logical equivalences involving conditional statements![\equiv (P \land [P\lor (Q \land \lnot Q)]) \lor(\lnot P \land \lnot [ P\lor (Q \land \lnot Q)])](/tpl/images/0284/9635/6e0c9.png)
by the Double negation law![\equiv (P \land [P\lor (Q \land \lnot Q)]) \lor(\lnot P \land \lnot P\land \lnot(Q \land \lnot Q))](/tpl/images/0284/9635/47ba2.png)
by De Morgan's law![\equiv (P \land [P\lor F]) \lor(\lnot P \land \lnot P\land \lnot(Q \land \lnot Q))](/tpl/images/0284/9635/540d2.png)
by the Negation law![\equiv (P \land [P\lor F]) \lor(\lnot P \land \lnot P\land \lnot Q \lor \lnot(\lnot Q))](/tpl/images/0284/9635/a3ec4.png)
by De Morgan's law![\equiv (P \land [P\lor F]) \lor(\lnot P \land \lnot P\land \lnot Q \lor Q)](/tpl/images/0284/9635/0bf03.png)
by the Double negation law
by the Identity law
by the Idempotent law
by the Commutative law
by the Negation law
by De Morgan's law
by the Idempotent law
by the Distributive law
by the Negation law
by the Domination law
![Prove that p (p) = (qa ~ q)] is a tautology.](/tpl/images/0284/9635/e6301.jpg)
Other questions on the subject: Mathematics
Mathematics, 21.06.2019 14:00, drelisech6467
Ben bowled 124 and 188 in his first two games. what must he bowl in his third game to have an average of at least 160?
Answers: 1
Mathematics, 21.06.2019 18:00, joseroblesrivera123
Since opening night, attendance at play a has increased steadily, while attendance at play b first rose and then fell. equations modeling the daily attendance y at each play are shown below, where x is the number of days since opening night. on what day(s) was the attendance the same at both plays? what was the attendance? play a: y = 8x + 191 play b: y = -x^2 + 26x + 126
Answers: 1
Mathematics, 21.06.2019 20:00, cferguson
Someone answer asap for ! the total ticket sales for a high school basketball game were $2,260. the ticket price for students were $2.25 less than the adult ticket price. the number of adult tickets sold was 230, and the number of student tickets sold was 180. what was the price of an adult ticket?
Answers: 1
You know the right answer?
Prove that p (p) = (qa ~ q)] is a tautology....
Questions in other subjects:
Computers and Technology, 11.01.2020 03:31
History, 11.01.2020 03:31
Mathematics, 11.01.2020 03:31
Mathematics, 11.01.2020 03:31
Physics, 11.01.2020 03:31
Law, 11.01.2020 03:31
Mathematics, 11.01.2020 03:31
