Truth table for: ( p → r) ⊕ ( q ↔ s)
in Other Math Topics by Level 2 User (1.0k points)

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I’m not sure what your symbols mean, so I’ll explain my assumptions first.

p→q: I take this to mean “p implies q”. That is, if p=1 (p is TRUE) then q=1 (TRUE). So I take (p→q) to mean that if p=0 then q must be zero, so if it isn’t the result is FALSE (0). This would give the truth table:

p q (p→q)

0 0     1

0 1     0

1 0     0

1 1      1

rs: I take this to mean that r and s are equivalent, so where r and s are the same, (rs)=1 and where they are different, (rs)=0, which seems to be the same as (p→q).

A different interpretation of (p→q) could be that, whatever q is, (p→q)=p giving us the truth table:

p q (p→q)

0 0    0

0 1     0

1 0     1

1 1      1

The third operator ⨁ I understand to be exclusive-OR, and the truth table is:

00=0,

01=1,

10=1,

11=0.

I hope this info helps you.

Example:

p q (p→q) r s (rs) (p→q)(rs)

1  1     1     1  0     0                  1

0  1    0     1  1      1                  1

This is just two rows out of the 16 rows making up the truth table. The remaining 14 rows depend on what → and mean as binary operators.

by Top Rated User (1.2m points)

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