Math Problem Solver

Sixathletesparticipateinthetournament:Liutauras,Arnas,Skirmantas,Linas,Tomas,Marius.

Onlyoneathletemaytakethesameplaceinthematch.

Fivesportslotteryplayerspredictedthefollowingresults:

1)Marius–first,Arnas–fifth;

2)Skirmantas–third,Liutauras–first;

3)Arnas–fifth,Tomas–fourth;

4)Liutauras–sixst,Linas–fifth;

5)Arnas–second,Skirmantas–fourth.

It isknownthateachplayerguessedat leastonetournamentresult.

1 Whowasfirst?

1 OLiutauras; 2 OLinas;

3 OSkirmantas; 4 OArnas;

5 OMarius; 6 OLiutaurasorLinas;

7 OArnasorLinas; 8 OMariusorLiutauras;

9 OMariusorLinas.

2 Whowassecond?

1 OArnasorLinas; 2OLinas;

3 OLiutauras; 4OLiutaurasorLinas;

5 OSkirmantas; 6OMarius;

7 OArnasorLiutauras; 8OLiutaurasorMarius;

9 OArnas.

3 Whowaslast?

1 OLiutauras; 2 OSkirmantas;

3 OTomas; 4 OLiutaurasorSkirmantas;

5 OLinas; 6 OLiutaurasorLinas;

7 OTomas; 8 OArnasorLiutauras;

9 OArnasorLinas.

4 WhatplacetookSkirmantas?

1 Ofirstorfourth; 2 Ofourth;

3 Ofirst; 4 Ofirstorthird;

5 Othirdorfourth; 6 Ofirstorsecond;

7 Osecondorfourth; 8 Othird;

9 Osecond.

5 WhatplacetookTomas?

1 Othirdorfourth; 2 Othird;

3 Osecondorfourth; 4 Osecond;

5 Ofirstorthird; 6 Ofirst;

7 Ofourth; 8 Ofirstorfourth;

9 Ofirstorsecond.

6 p 0 = 1 O0; 2 Op; 3 O1; 4Op.

7 Whichlogicaloperation( ) isdefinedinthetable?

z w z w

0 0 0

0 1 1

1 0 1

1 1 0

1 Oz w; 2 Oz w;

3 Ozw; 4 Oz&w;

5 Oz w; 6 Oz w.

8 w&v r y=

1O(w&(v r)) y;

2Ow&((v r) y);

3O((w&v) r) y;

4O(w&v) (r y);

5Ow&(v (r y)).

9 1. y y A. y

2. y&w B. w&y

3. y y C. 1

1 OABC; 2 OBCA;

3 OCAB; 4 OBAC;

5 OACB; 6 OCBA.

10 1. r r A. r

2. r r B. 1

3. r r C. r

1 OCAB; 2OBCA;

3 OACB; 4OABC;

5 OBAC; 6OCBA.

11

Whichformula

istautology?

(F)t t;

(R)t t;

1 O(R) ;

2 Oboth;

3 O(F) ;

4 Onoone.

12

Whichformula

iscontradiction?

(Q)y y;

(F)0&y;

1 Oboth;

2 Onoone;

3 O(Q) ;

4 O(F) .

13 1. z&z A. doublenegation

2. z z B. thirdimpossible

3. z z C. contradiction

1 OCAB; 2 OBAC;

3 OACB; 4 OCBA;

5 OBCA; 6 OABC