DEPARTMENT OF MATHEMATICS

 

Mathematical Logic

 

1st Tutorial Problems

 

 

 

 

1.            They're both tautologies. Here's the truth table for 

                           (ii) (((P1 Þ P2) Þ P1) Þ P1).

   

                            P1    P2    (P1 Þ P2)    (P1 Þ P2) Þ P1)    (((P1 Þ P2) Þ P1) Þ P1)

                            1    1            1                                1                                        1

                            1    0            0                                1                                        1

                            0    1            1                                0                                        1

                            0    0            1                                0                                        1

            

 

2.         (i) (last part):

 

                            P1    P2    P3    (if P1 then P2 else P3)    (P1 Þ P2)    (~P1 Þ P3)    ((P1 Þ P2) & (~P1 Þ P3))

                            1    1      1                  1                              1                    1                            1    

                            1    1      0                  1                              1                    1                            1

                            1    0      1                  0                              0                    1                            0

                            1    0      0                  0                              0                    1                            0

                            0    1      1                  1                              1                    1                            1

                            0    1      0                  0                              1                    0                            0

                            0    0      1                  1                              1                    1                            1

                            0    0      0                  0                              1                    0                            0

 

(ii) 

 

                            P1    P2    P3    (if P1 then P1 else P1)    (if P1 then P2 else P3)    (if (if ...) then P3 else P2)

                            1    1      1                  1                                  1                                          1    

                            1    1      0                  1                                  1                                          0

                            1    0      1                  1                                  0                                          0

                            1    0      0                  1                                  0                                          0

                            0    1      1                  0                                  1                                          1

                            0    1      0                  0                                  0                                          1

                            0    0      1                  0                                  1                                          1

                            0    0      0                  0                                  0                                          0