4 replaced http://philosophy.stackexchange.com/ with https://philosophy.stackexchange.com/
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Per this answer, 'A is sufficient for B.`   means that    'A is a subset of B'.

A picture and real-life example may aid to understand the followingthe following:

Your main question is whether (2) follows from (1);

(1) P → Q [ P is a sufficient condition for Q ],

(2) Q → P [ P is a necessary condition for Q ].

The reason the entailment from (1) to (2) doesn't hold is that it's possible that Q follow from some proposition R that is not equivalent to P. The only instance where the entailment is realized is one where all necessary conditions for Q are logically equivalent to P.

The above is exemplified in the picture below, if P = Northern Ireland, Q = UK, R = Great Britain.

Then being in Northern Ireland is sufficient for being in the UK,
but is NOT necessary for being in the UK, because one can also be in U.K. by being in
Great Britain.
enter image description here

Per this answer, 'A is sufficient for B.`   means that    'A is a subset of B'.

A picture and real-life example may aid to understand the following:

Your main question is whether (2) follows from (1);

(1) P → Q [ P is a sufficient condition for Q ],

(2) Q → P [ P is a necessary condition for Q ].

The reason the entailment from (1) to (2) doesn't hold is that it's possible that Q follow from some proposition R that is not equivalent to P. The only instance where the entailment is realized is one where all necessary conditions for Q are logically equivalent to P.

The above is exemplified in the picture below, if P = Northern Ireland, Q = UK, R = Great Britain.

Then being in Northern Ireland is sufficient for being in the UK,
but is NOT necessary for being in the UK, because one can also be in U.K. by being in
Great Britain.
enter image description here

Per this answer, 'A is sufficient for B.`   means that    'A is a subset of B'.

A picture and real-life example may aid to understand the following:

Your main question is whether (2) follows from (1);

(1) P → Q [ P is a sufficient condition for Q ],

(2) Q → P [ P is a necessary condition for Q ].

The reason the entailment from (1) to (2) doesn't hold is that it's possible that Q follow from some proposition R that is not equivalent to P. The only instance where the entailment is realized is one where all necessary conditions for Q are logically equivalent to P.

The above is exemplified in the picture below, if P = Northern Ireland, Q = UK, R = Great Britain.

Then being in Northern Ireland is sufficient for being in the UK,
but is NOT necessary for being in the UK, because one can also be in U.K. by being in
Great Britain.
enter image description here

3 replaced http://math.stackexchange.com/ with https://math.stackexchange.com/
source | link

Per this answerthis answer, 'A is sufficient for B.`   means that    'A is a subset of B'.

A picture and real-life example may aid to understand the following:

Your main question is whether (2) follows from (1);

(1) P → Q [ P is a sufficient condition for Q ],

(2) Q → P [ P is a necessary condition for Q ].

The reason the entailment from (1) to (2) doesn't hold is that it's possible that Q follow from some proposition R that is not equivalent to P. The only instance where the entailment is realized is one where all necessary conditions for Q are logically equivalent to P.

The above is exemplified in the picture below, if P = Northern Ireland, Q = UK, R = Great Britain.

Then being in Northern Ireland is sufficient for being in the UK,
but is NOT necessary for being in the UK, because one can also be in U.K. by being in
Great Britain.
enter image description here

Per this answer, 'A is sufficient for B.`   means that    'A is a subset of B'.

A picture and real-life example may aid to understand the following:

Your main question is whether (2) follows from (1);

(1) P → Q [ P is a sufficient condition for Q ],

(2) Q → P [ P is a necessary condition for Q ].

The reason the entailment from (1) to (2) doesn't hold is that it's possible that Q follow from some proposition R that is not equivalent to P. The only instance where the entailment is realized is one where all necessary conditions for Q are logically equivalent to P.

The above is exemplified in the picture below, if P = Northern Ireland, Q = UK, R = Great Britain.

Then being in Northern Ireland is sufficient for being in the UK,
but is NOT necessary for being in the UK, because one can also be in U.K. by being in
Great Britain.
enter image description here

Per this answer, 'A is sufficient for B.`   means that    'A is a subset of B'.

A picture and real-life example may aid to understand the following:

Your main question is whether (2) follows from (1);

(1) P → Q [ P is a sufficient condition for Q ],

(2) Q → P [ P is a necessary condition for Q ].

The reason the entailment from (1) to (2) doesn't hold is that it's possible that Q follow from some proposition R that is not equivalent to P. The only instance where the entailment is realized is one where all necessary conditions for Q are logically equivalent to P.

The above is exemplified in the picture below, if P = Northern Ireland, Q = UK, R = Great Britain.

Then being in Northern Ireland is sufficient for being in the UK,
but is NOT necessary for being in the UK, because one can also be in U.K. by being in
Great Britain.
enter image description here

2 added 184 characters in body
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Per this answer, 'A is sufficient for B.`
     means that
'B is a bigger set, and A    'A is a subset of B'.

A picture and real-life example may aid to understand the following:

Your main question is whether (2) follows from (1);

(1) P → Q [ P is a sufficient condition for Q ],

(2) Q → P [ P is a necessary condition for Q ].

The reason the entailment from (1) to (2) doesn't hold is that it's possible that Q follow from some proposition R that is not equivalent to P. The only instance where the entailment is realized is one where all necessary conditions for Q are logically equivalent to P.

The above is exemplified in the picture below, if you consider P = WalesNorthern Ireland, Q = Great BritainUK, R = WalesGreat Britain.

Then being in Northern Ireland is sufficient for being in the UK,
but is NOT necessary for being in the UK, because one can also be in U.K. by being in
Great Britain.
enter image description here

Per this answer, 'A is sufficient for B.`
 means that
'B is a bigger set, and A is a subset of B'.

A picture and real-life example may aid to understand the following:

Your main question is whether (2) follows from (1);

(1) P → Q [ P is a sufficient condition for Q ],

(2) Q → P [ P is a necessary condition for Q ].

The reason the entailment from (1) to (2) doesn't hold is that it's possible that Q follow from some proposition R that is not equivalent to P. The only instance where the entailment is realized is one where all necessary conditions for Q are logically equivalent to P.

The above is exemplified in the picture below, if you consider P = Wales, Q = Great Britain, R = Wales.

enter image description here

Per this answer, 'A is sufficient for B.`    means that    'A is a subset of B'.

A picture and real-life example may aid to understand the following:

Your main question is whether (2) follows from (1);

(1) P → Q [ P is a sufficient condition for Q ],

(2) Q → P [ P is a necessary condition for Q ].

The reason the entailment from (1) to (2) doesn't hold is that it's possible that Q follow from some proposition R that is not equivalent to P. The only instance where the entailment is realized is one where all necessary conditions for Q are logically equivalent to P.

The above is exemplified in the picture below, if P = Northern Ireland, Q = UK, R = Great Britain.

Then being in Northern Ireland is sufficient for being in the UK,
but is NOT necessary for being in the UK, because one can also be in U.K. by being in
Great Britain.
enter image description here

1
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