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what does it have to do with plucking grain on shabbat?

We keep the Sabbath holy by keeping the first commandment.

"Hear, O Israel! The Lord our God, The Lord is One; Thou shalt love the Lord thy God with all thy heart, and with all thy soul, and with all thy mind."

By placing God in the first place of our lives and worshipping God with all of our hearts, mind, soul, and strength we keep the Sabbath holy.

That is the commandment given by God. There is nothing in the Commandments about plucking grain.

Jesus said, "Do not think that I came to abolish the Law or the Prophets; I did not come to abolish but to fulfill. (Matthew 5:17)

keeping shabbat holy is a specific commandment involving not doing any labor or lighting fire.

That is not a commandment. It is part of the law of Moses.

laws=commandments

The Ten Commandments were placed inside the ark of the covenant.
The book of the law (600+ laws) , and put it in the side of the ark of the
covenant.

laws and commandments is the same thing. If Go'd commands it, it's the law.

The Torah explicitly prohibits lighting a fire ( Exodus 35:23) and field work such as plowing and harvesting (Exodus 34:20) on Shabbat.

How does one 'fulfill' shabbat by ignoring its laws?