持つ
mo-tsu
Why milk that lasts is milk that holds
The picture A hand grips something and does not let go, so it stays on your side. 持つ keeps the grip; 置く takes the hand away and leaves the thing where it sits.
Where the picture shows up in 持つ
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Holding in the hand
かばんを持ちましょうか。
kaban o mochi-mashō ka
Shall I carry your bag?
Fingers wrap around the handle of someone else's bag and lift it.
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Holding it along with you
保険証を持って来てください。
hokenshō o motte kite kudasai
Please bring your insurance card.
The insurance card stays in your hand as that hand leaves the house and goes to the clinic.
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Still holding it
車を持っていますか。
kuruma o motte imasu ka
Do you have a car?
You keep hold of the car key for years and never let it go.
Never letting go of it is exactly how ownership is pictured.
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Holding out, not giving way
この牛乳は明日まで持ちます。
kono gyūnyū wa ashita made mochi-masu
This milk will last until tomorrow.
The milk holds its own condition against spoiling, gripping it tight until tomorrow.
Food lasting is the same hand: it keeps its grip and does not give up.
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Taking the cost on yourself
ここは私が持ちます。
koko wa watashi ga mochi-masu
I will get this one.
The bill lands on the table and your hand takes hold of it first.
All of it in one picture
持つ is one hand that grips and does not let go. Grip the handle and you are carrying; go along with the grip and you are bringing it; keep the key for years and you own a car; let the milk grip its own state and it lasts; grip the bill first and you are paying. So anything with 持つ carries the same feeling: as long as nothing lets go, the thing stays on your side.