How to tell if this propositional logic statement is valid?
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$$W ∧ X ∧ Y ⊨ Z text{ if and only if } ⊨ W → (X → (Y → Z))$$
I know it can be done using truth tables but I'm stuck on the "if and only if ⊨", I don't understand what that means.
logic propositional-calculus
edited Nov 23 at 15:23
Mauro ALLEGRANZA
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asked Nov 23 at 14:58
esperski
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up vote
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favorite
$$W ∧ X ∧ Y ⊨ Z text{ if and only if } ⊨ W → (X → (Y → Z))$$
I know it can be done using truth tables but I'm stuck on the "if and only if ⊨", I don't understand what that means.
logic propositional-calculus
edited Nov 23 at 15:23
Mauro ALLEGRANZA
63.6k448110
asked Nov 23 at 14:58
esperski
2
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
$$W ∧ X ∧ Y ⊨ Z text{ if and only if } ⊨ W → (X → (Y → Z))$$
I know it can be done using truth tables but I'm stuck on the "if and only if ⊨", I don't understand what that means.
logic propositional-calculus
edited Nov 23 at 15:23
Mauro ALLEGRANZA
63.6k448110
asked Nov 23 at 14:58
esperski
2
$$W ∧ X ∧ Y ⊨ Z text{ if and only if } ⊨ W → (X → (Y → Z))$$
I know it can be done using truth tables but I'm stuck on the "if and only if ⊨", I don't understand what that means.
logic propositional-calculus
logic propositional-calculus
edited Nov 23 at 15:23
Mauro ALLEGRANZA
63.6k448110
asked Nov 23 at 14:58
esperski
2
edited Nov 23 at 15:23
Mauro ALLEGRANZA
63.6k448110
asked Nov 23 at 14:58
esperski
2
edited Nov 23 at 15:23
Mauro ALLEGRANZA
63.6k448110
edited Nov 23 at 15:23
Mauro ALLEGRANZA
63.6k448110
edited Nov 23 at 15:23
Mauro ALLEGRANZA
63.6k448110
63.6k448110
asked Nov 23 at 14:58
esperski
2
asked Nov 23 at 14:58
esperski
2
asked Nov 23 at 14:58
esperski
2
2
add a comment |
add a comment |
1 Answer
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'A if and only if B' is written symbolically as $ A iff B$ and it means that whenever A happens B happens too and whenever $B$ happens $A$ happens too. It is just math talk for: "these things imply one another." Your truth table calculations should reveal that these two things always imply one another.
answered Nov 23 at 15:03
Mason
1,9031426
add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
0
down vote
'A if and only if B' is written symbolically as $ A iff B$ and it means that whenever A happens B happens too and whenever $B$ happens $A$ happens too. It is just math talk for: "these things imply one another." Your truth table calculations should reveal that these two things always imply one another.
answered Nov 23 at 15:03
Mason
1,9031426
add a comment |
up vote
0
down vote
'A if and only if B' is written symbolically as $ A iff B$ and it means that whenever A happens B happens too and whenever $B$ happens $A$ happens too. It is just math talk for: "these things imply one another." Your truth table calculations should reveal that these two things always imply one another.
answered Nov 23 at 15:03
Mason
1,9031426
add a comment |
up vote
0
down vote
up vote
0
down vote
'A if and only if B' is written symbolically as $ A iff B$ and it means that whenever A happens B happens too and whenever $B$ happens $A$ happens too. It is just math talk for: "these things imply one another." Your truth table calculations should reveal that these two things always imply one another.
answered Nov 23 at 15:03
Mason
1,9031426
'A if and only if B' is written symbolically as $ A iff B$ and it means that whenever A happens B happens too and whenever $B$ happens $A$ happens too. It is just math talk for: "these things imply one another." Your truth table calculations should reveal that these two things always imply one another.
answered Nov 23 at 15:03
Mason
1,9031426
answered Nov 23 at 15:03
Mason
1,9031426
answered Nov 23 at 15:03
Mason
1,9031426
answered Nov 23 at 15:03
Mason
1,9031426
1,9031426
add a comment |
add a comment |
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